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Relevant bibliographies by topics / Selmer group

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Academic literature on the topic 'Selmer group'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Selmer group"

1

Česnavičius, Kęstutis. "Selmer groups and class groups." Compositio Mathematica 151, no. 3 (2014): 416–34. http://dx.doi.org/10.1112/s0010437x14007441.

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AbstractLet $A$ be an abelian variety over a global field $K$ of characteristic $p\geqslant 0$. If $A$ has nontrivial (respectively full) $K$-rational $l$-torsion for a prime $l\neq p$, we exploit the fppf cohomological interpretation of the $l$-Selmer group $\text{Sel}_{l}\,A$ to bound $\#\text{Sel}_{l}\,A$ from below (respectively above) in terms of the cardinality of the $l$-torsion subgroup of the ideal class group of $K$. Applied over families of finite extensions of $K$, the bounds relate the growth of Selmer groups and class groups. For function fields, this technique proves the unbound

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Kundu, Debanjana. "Growth of Fine Selmer Groups in Infinite Towers." Canadian Mathematical Bulletin 63, no. 4 (2020): 921–36. http://dx.doi.org/10.4153/s0008439520000168.

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AbstractIn this paper, we study the growth of fine Selmer groups in two cases. First, we study the growth of fine Selmer ranks in multiple $\mathbb{Z}_{p}$-extensions. We show that the growth of the fine Selmer group is unbounded in such towers. We recover a sufficient condition to prove the $\unicode[STIX]{x1D707}=0$ conjecture for cyclotomic $\mathbb{Z}_{p}$-extensions. We show that in certain non-cyclotomic $\mathbb{Z}_{p}$-towers, the $\unicode[STIX]{x1D707}$-invariant of the fine Selmer group can be arbitrarily large. Second, we show that in an unramified $p$-class field tower, the growth

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DOKCHITSER, TIM, and VLADIMIR DOKCHITSER. "Self-duality of Selmer groups." Mathematical Proceedings of the Cambridge Philosophical Society 146, no. 2 (2009): 257–67. http://dx.doi.org/10.1017/s0305004108001989.

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AbstractThe first part of the paper gives a new proof of self-duality for Selmer groups: if A is an abelian variety over a number field K, and F/K is a Galois extension with Galois group G, then the $\Q_p$G-representation naturally associated to the p∞-Selmer group of A/F is self-dual. The second part describes a method for obtaining information about parities of Selmer ranks from the local Tamagawa numbers of A in intermediate extensions of F/K.

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Wuthrich, Christian. "Iwasawa theory of the fine Selmer group." Journal of Algebraic Geometry 16, no. 1 (2007): 83–108. http://dx.doi.org/10.1090/s1056-3911-06-00436-x.

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Lai, King Fai, Ignazio Longhi, Ki-Seng Tan, and Fabien Trihan. "An example of non-cotorsion Selmer group." Proceedings of the American Mathematical Society 143, no. 6 (2015): 2355–64. http://dx.doi.org/10.1090/s0002-9939-2015-12459-8.

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ZERBES, SARAH LIVIA. "Akashi series of Selmer groups." Mathematical Proceedings of the Cambridge Philosophical Society 151, no. 2 (2011): 229–43. http://dx.doi.org/10.1017/s0305004111000211.

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AbstractWe study the Selmer group of an elliptic curve over an admissible p-adic Lie extension of a number field F. We give a formula for the Akashi series attached to this module, in terms of the corresponding objects for the cyclotomic ℤp-extension and certain correction terms. This extends our earlier work [16], in particular since it applies to elliptic curves having split multiplicative reduction at some primes above p, in which case the Akashi series can have additional zeros.

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SWINNERTON–DYER, PETER. "The effect of twisting on the 2-Selmer group." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 3 (2008): 513–26. http://dx.doi.org/10.1017/s0305004108001588.

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AbstractLet Γ be an elliptic curve defined over Q, all of whose 2-division points are rational, and let Γb be its quadratic twist by b. Subject to a mild additional condition on Γ, we find the limit of the probability distribution of the dimension of the 2-Selmer group of Γb as the number of prime factors of b increases; and we show that this distribution depends only on whether the 2-Selmer group of Γ has odd or even dimension.

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BARTEL, ALEX. "Large Selmer groups over number fields." Mathematical Proceedings of the Cambridge Philosophical Society 148, no. 1 (2009): 73–86. http://dx.doi.org/10.1017/s0305004109990132.

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AbstractLet p be a prime number and M a quadratic number field, M ≠ ℚ() if p ≡ 1 mod 4. We will prove that for any positive integer d there exists a Galois extension F/ℚ with Galois group D2p and an elliptic curve E/ℚ such that F contains M and the p-Selmer group of E/F has size at least pd.

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Lim, Meng Fai. "A remark on the 𝔐H(G)-conjecture and Akashi series". International Journal of Number Theory 11, № 01 (2014): 269–97. http://dx.doi.org/10.1142/s1793042115500165.

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In this paper, we give a criterion for the dual Selmer group of an elliptic curve which has either good ordinary reduction or multiplicative reduction at every prime above p to satisfy the 𝔐H(G)-conjecture. As a by-product of our calculations, we are able to define the Akashi series of the dual Selmer groups assuming the conjectures of Mazur and Schneider. Previously, the Akashi series are defined under the stronger assumption that the dual Selmer group satisfies the 𝔐H(G)-conjecture. We then establish a criterion for the vanishing of the dual Selmer groups using the Akashi series. We will app

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Lim, Meng Fai. "On the pseudo-nullity of the dual fine Selmer groups." International Journal of Number Theory 11, no. 07 (2015): 2055–63. http://dx.doi.org/10.1142/s1793042115500888.

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In this paper, we will study the pseudo-nullity of the dual fine Selmer group and its related question. We investigate certain situations, where one can deduce the pseudo-nullity of the dual fine Selmer group of a general Galois module over an admissible p-adic Lie extension F∞ from the knowledge of the pseudo-nullity of the Galois group of the maximal abelian unramified pro-p extension of F∞ at which every prime of F∞ above p splits completely. In particular, this gives us a way to construct examples of the pseudo-nullity of the dual fine Selmer group of a Galois module that is unramified out

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Dissertations / Theses on the topic "Selmer group"

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Wuthrich, Christian. "The fine Selmer group and height pairings." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616068.

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Mailhot, James Michael. "Selmer groups for elliptic curves with isogenies of prime degree /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/5801.

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Djabri, Zafer M. "P-descent on elliptic curves over number fields." Thesis, University of Kent, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.310161.

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van, Beek Monique. "Computing the Cassels-Tate pairing." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/252852.

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Česnavičius, Kęstutis. "Selmer groups as flat cohomology groups." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90180.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 44-46).<br>Given a prime number p, Bloch and Kato showed how the p Selmer group of an abelian variety A over a number field K is determined by the p-adic Tate module. In general, the pm1-Selmer group Selpmn A need not be determined by the mod pm Galois representation A[pm]; we show, however, that this is the case if p is large enough. More precisely, we exhibit a finite explicit set of rational primes E depending on K and

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Drinen, Michael Jeffrey. "Iwasawa mu-invariants of Selmer groups /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5810.

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Zerbes, Sarah. "Selmer groups over p-adic Lie extensions." Thesis, University of Cambridge, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613792.

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McConnell, Gary. "On the Iwasawa theory of elliptic curves over cyclotomic fields." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307064.

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Livingstone, Boomla Alice Jane. "Selmer groups, zeta elements and refined Stark conjectures." Thesis, King's College London (University of London), 2018. https://kclpure.kcl.ac.uk/portal/en/theses/selmer-groups-zeta-elements-and-refined-stark-conjectures(0ecef088-5829-4e5b-a35d-974c505136d9).html.

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In this thesis we study explicit connections between the values at s = 0 of the higher derivatives of Dirichlet L-functions and the higher Fitting ideals of Selmer groups of the multiplicative group over finite abelian extensions of number fields. We also prove new structural results for such Selmer groups, showing that their higher Fitting ideals admit natural direct sum decompositions. The first of our main results allows us to show that certain canonical invariants that are associated to (generalised) Rubin-Stark elements by Valli`eres in [28] can be completely, though in general only conje

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Brau, Julio. "Selmer groups of elliptic curves and Galois representations." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708896.

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Books on the topic "Selmer group"

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Gaëtan, Chenevier, ed. Families of Galois representations and Selmer groups. Société mathématique de France, 2009.

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Hejhal, Dennis A. Eigenvalues of the Laplacian for Hecke triangle groups. American Mathematical Society, 1992.

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Hejhal, Dennis A. Regular b-groups, degenerating Riemann surfaces, and spectral theory. American Mathematical Society, 1990.

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Elstrodt, J. Groups acting on hyperbolic space: Harmonic analysis and number theory. Springer, 1998.

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5

Mandouvalos, Nikolaos. Scattering operator, Eisenstein series, inner product formula, and "Maass-Selberg" relations for Kleinian groups. American Mathematical Society, 1989.

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6

Selden, John. John Selden on Jewish marriage law: The Uxor Hebraica. E.J. Brill, 1990.

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7

The Richard & Judy book club reader: Popular texts and the practices of reading. Ashgate, 2011.

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8

D, Goldfeld, ed. Collected works of Hervé Jacquet. American Mathematical Society, 2011.

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9

Barnett, Alex, 1972 December 7- editor of compilation, ed. Spectral geometry. American Mathematical Society, 2012.

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10

Bombieri, Enrico, and Karl Egil Aubert. Number Theory, Trace Formulas, and Discrete Groups: Symposium in Honor of Atle Selberg, Oslo, Norway, July 14-21, 1987. Academic Pr, 1989.

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Book chapters on the topic "Selmer group"

1

Bilu, Yuri F., Yann Bugeaud, and Maurice Mignotte. "Selmer Group and Proof of Catalan’s Conjecture." In The Problem of Catalan. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10094-4_11.

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Li, Xiangling. "The Stupid Egg Seller." In Advances in Group Decision and Negotiation. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-007-0989-8_18.

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Greenberg, Ralph. "On the Structure of Selmer Groups." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45032-2_6.

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4

Sujatha, R., and M. Witte. "Fine Selmer Groups and Isogeny Invariance." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97379-1_19.

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Kranton, Rachel E., and Deborah F. Minehart. "A Theory of Buyer-Seller Networks." In Networks and Groups. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-24790-6_16.

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Kranton, Rachel E., and Deborah F. Minehart. "Competition for Goods in Buyer-Seller Networks." In Networks and Groups. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-24790-6_17.

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Cattani, Kara, Derek Griner, David M. Erekson, Gary M. Burlingame, Mark E. Beecher, and Cameron T. Alldredge. "Module 6: Multiple Selves." In Compassion Focused Group Therapy for University Counseling Centers. Routledge, 2021. http://dx.doi.org/10.4324/9781003202486-6.

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Coates, J., and R. Sujatha. "Fine Selmer groups for elliptic curves with complex multiplication." In Algebra and Number Theory. Hindustan Book Agency, 2005. http://dx.doi.org/10.1007/978-93-86279-23-1_22.

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Bloch, Francis, and Sayantan Ghosal. "Buyers’ and Sellers’ Cartels on Markets With Indivisible Goods." In Networks and Groups. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-24790-6_18.

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Kurihara, Masato. "The Structure of Selmer Groups of Elliptic Curves and Modular Symbols." In Contributions in Mathematical and Computational Sciences. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-55245-8_11.

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Conference papers on the topic "Selmer group"

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Li, Bin, Dong Hao, Dengji Zhao, and Tao Zhou. "Customer Sharing in Economic Networks with Costs." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/51.

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In an economic market, sellers, infomediaries and customers constitute an economic network. Each seller has her own customer group and the seller's private customers are unobservable to other sellers. Therefore, a seller can only sell commodities among her own customers unless other sellers or infomediaries share her sale information to their customer groups. However, a seller is not incentivized to share others' sale information by default, which leads to inefficient resource allocation and limited revenue for the sale. To tackle this problem, we develop a novel mechanism called customer shar

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Greenberg, Ralph. "Selmer Groups and Congruences." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0048.

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Kotut, Lindah, Timothy L. Stelter, Michael Horning, and D. Scott McCrickard. "Willing Buyer, Willing Seller." In GROUP '20: The 2020 ACM International Conference on Supporting Group Work. ACM, 2020. http://dx.doi.org/10.1145/3323994.3369899.

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Christozov, Dimitar, and Plamen Mateev. "Warranty as a Factor for E-commerce Success." In 2003 Informing Science + IT Education Conference. Informing Science Institute, 2003. http://dx.doi.org/10.28945/2641.

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Two groups of factors impact the success of e-commerce transaction: environmental factors and content of the messages exchanged between the seller and the buyer. The first group includes factors describing the environment in which the seller-buyer relationship operates, such as IT infrastructure, Logistic Infrastructure, Financial Infrastructure, and Government regulations. Second group -- content of the message -- covers these elements of the message, which improve the trust between the two parties (especially the buyer’s trust). Among them, the statement about warranty plays critical role as

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Guan, Lei. "Comparison of group-buying sales effort between the seller and buyers." In 2017 14th International Conference on Service Systems and Service Management (ICSSSM). IEEE, 2017. http://dx.doi.org/10.1109/icsssm.2017.7996184.

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Štefko, Róbert, Miroslav Frankovský, Jana Kovaľová, Zuzana Birknerová, and Lucia Zbihlejová. "Assessment of sellers’ manipulative behavior by customers and sellers in the context of generations X, Y and Z." In 11th International Scientific Conference „Business and Management 2020“. VGTU Technika, 2020. http://dx.doi.org/10.3846/bm.2020.530.

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In the field of business and trade, we encounter concepts of manipulation and persuasion in the sense of trying to convince someone by applying certain pressure to the mind, opinions, emotions, and behavior, with an aim to cause change. However, literature provides only little information aimed specifically at the manipulative approach of sellers to customers. The purpose of the presented paper is, therefore, to study manipulative behavior of sellers as one of the important determinants of success in business behavior. The research focuses on assessing the manipulative behavior of sellers by c

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Richardson, Lorna, Colette Parfitt, Emma Kirk, Rachael Stevenson, and Tracey Taylor. "P-207 Regenerate our own true selves (roots) model of group therapy." In Leading, Learning and Innovating, Hospice UK 2017 National Conference, 22–24 November 2017, Liverpool. British Medical Journal Publishing Group, 2017. http://dx.doi.org/10.1136/bmjspcare-2017-hospice.232.

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Morik, Marco, Ashudeep Singh, Jessica Hong, and Thorsten Joachims. "Controlling Fairness and Bias in Dynamic Learning-to-Rank (Extended Abstract)." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/655.

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Rankings are the primary interface through which many online platforms match users to items (e.g. news, products, music, video). In these two-sided markets, not only do the users draw utility from the rankings, but the rankings also determine the utility (e.g. exposure, revenue) for the item providers (e.g. publishers, sellers, artists, studios). It has already been noted that myopically optimizing utility to the users -- as done by virtually all learning-to-rank algorithms -- can be unfair to the item providers. We, therefore, present a learning-to-rank approach for explicitly enforcing merit

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Christozov, Dimitar, Stefanka Chukova, and Plamen Mateev. "The Risk of Misinforming for Competing Messages." In InSITE 2009: Informing Science + IT Education Conference. Informing Science Institute, 2009. http://dx.doi.org/10.28945/3329.

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This paper extends previous studies on quantifying the risk of misinforming by introducing models, which allow measuring the risk of misinforming in case of competing messages. These models are realistic representation of the market situation, where purchasing decisions are made based on the assessment of all available offers and selecting the one that meets at most the buyer's needs. The paper emphasizes the case of two competing products offered to a group of potential clients and studies the risk of misinforming and its effect on the purchase decisions. In addition, models for the evaluatio

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Savrda, Charles E., Carleton Foster, and Colt Morton. "ICHNOSEDIMENTOLOGIC COMPARISON OF CARBONATE DEPOSITIONAL RHYTHMS IN CRETACEOUS SELMA GROUP CHALKS, EASTERN GULF COASTAL PLAIN." In GSA Annual Meeting in Phoenix, Arizona, USA - 2019. Geological Society of America, 2019. http://dx.doi.org/10.1130/abs/2019am-334766.

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Reports on the topic "Selmer group"

1

Mascagni, Giulia, Roel Dom, and Fabrizio Santoro. The VAT in Practice: Equity, Enforcement and Complexity. Institute of Development Studies (IDS), 2021. http://dx.doi.org/10.19088/ictd.2021.002.

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The value added tax (VAT) is supposed to be a tax on consumption that achieves greater economic efficiency than alternative indirect taxes. It is also meant to facilitate enforcement through the ‘self-enforcing mechanism’ – based on opposed incentives for buyers and sellers, and because of the paper trail it creates. Being a rather sophisticated tax, however, the VAT is complex to administer and costly to comply with, especially in lower-income countries. This paper takes a closer look at how the VAT system functions in practice in Rwanda. Using a mixed-methods approach, which combines qualita

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