Relevant bibliographies by topics / Iwasawa's

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Academic literature on the topic 'Iwasawa's'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Iwasawa's"

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KADOKAMI, TERUHISA, and YASUSHI MIZUSAWA. "IWASAWA TYPE FORMULA FOR COVERS OF A LINK IN A RATIONAL HOMOLOGY SPHERE." Journal of Knot Theory and Its Ramifications 17, no. 10 (October 2008): 1199–221. http://dx.doi.org/10.1142/s0218216508006580.

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Based on the analogy between links and primes, we present an analogue of the Iwasawa's class number formula in a Zp-extension for the p-homology groups of pn-fold cyclic covers of a link in a rational homology 3-sphere. We also describe the associated Iwasawa invariants precisely for some examples and discuss analogies with the number field case.
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SCHETTLER, JORDAN. "GENERALIZATIONS OF IWASAWA'S "RIEMANN–HURWITZ" FORMULA FOR CYCLIC p-EXTENSIONS OF NUMBER FIELDS." International Journal of Number Theory 10, no. 01 (January 22, 2014): 219–33. http://dx.doi.org/10.1142/s1793042113500905.

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We produce generalizations of Iwasawa's "Riemann–Hurwitz" formula for number fields. These generalizations apply to cyclic extensions of number fields of degree pn for any positive integer n. We first deduce some congruences and inequalities and then use these formulas to establish a vanishing criterion for Iwasawa λ-invariants which generalizes a result of Fukuda et al. for totally real number fields.
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HAJIR, FARSHID, and CHRISTIAN MAIRE. "Prime decomposition and the Iwasawa MU-invariant." Mathematical Proceedings of the Cambridge Philosophical Society 166, no. 3 (April 26, 2018): 599–617. http://dx.doi.org/10.1017/s0305004118000191.

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AbstractFor Γ = ℤp, Iwasawa was the first to construct Γ-extensions over number fields with arbitrarily large μ-invariants. In this work, we investigate other uniform pro-p groups which are realisable as Galois groups of towers of number fields with arbitrarily large μ-invariant. For instance, we prove that this is the case if p is a regular prime and Γ is a uniform pro-p group admitting a fixed-point-free automorphism of odd order dividing p−1. Both in Iwasawa's work, and in the present one, the size of the μ-invariant appears to be intimately related to the existence of primes that split completely in the tower.
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Belliard, Jean-Robert. "Global Units Modulo Circular Units: Descent Without Iwasawa’s Main Conjecture." Canadian Journal of Mathematics 61, no. 3 (June 1, 2009): 518–33. http://dx.doi.org/10.4153/cjm-2009-027-0.

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Abstract.Iwasawa's classical asymptotical formula relates the orders of the p-parts Xn of the ideal class groups along a ℤp-extension F∞/F of a number field F to Iwasawa structural invariants ƛ and μ attached to the inverse limit X∞ = . It relies on “good” descent properties satisfied by Xn. If F is abelian and F∞ is cyclotomic, it is known that the p-parts of the orders of the global units modulo circular units Un/Cn are asymptotically equivalent to the p-parts of the ideal class numbers. This suggests that these quotientsUn/Cn, so to speak unit class groups, also satisfy good descent properties. We show this directly, i.e., without using Iwasawa's Main Conjecture.
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Sands, Jonathan W. "Kummer's and Iwasawa's Version of Leopoldt's Conjecture." Canadian Mathematical Bulletin 31, no. 3 (September 1, 1988): 338–46. http://dx.doi.org/10.4153/cmb-1988-049-0.

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AbstractWe present a refinement of Iwasawa's approach to Leopoldt's conjecture on the non-vanishing of the p-adic regulator of an algebraic number field K. As an application, the conjecture for K implies the conjecture for a solvable extension L of degree g over K if g is relatively prime to p — 1 and p does not divide g, the discriminant of K, and the quotient of class numbers where is a primitive pth root of unity. This can be viewed as generalizing a theorem of Kummer on cyclotomic units.
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Schindler, Werner. "Iwasawa's Theorem and Integrals on Lie Groups." Mathematische Nachrichten 162, no. 1 (1993): 315–27. http://dx.doi.org/10.1002/mana.19931620122.

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Fukuda, Takashi. "Iwasawa's $\lambda $-invariants of certain real quadratic fields." Proceedings of the Japan Academy, Series A, Mathematical Sciences 65, no. 7 (1989): 260–62. http://dx.doi.org/10.3792/pjaa.65.260.

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Ochiai, Tadashi, and Kazuma Shimomoto. "Bertini theorem for normality on local rings in mixed characteristic (applications to characteristic ideals)." Nagoya Mathematical Journal 218 (June 2015): 125–73. http://dx.doi.org/10.1017/s0027763000027045.

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AbstractIn this article, we prove a strong version of the local Bertini theorem for normality on local rings in mixed characteristic. The main result asserts that a generic hyperplane section of a normal, Cohen–Macaulay, and complete local domain of dimension at least 3 is normal. Applications include the study of characteristic ideals attached to torsion modules over normal domains, which is fundamental in the study of Euler system theory, Iwasawa's main conjectures, and the deformation theory of Galois representations.
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Ochiai, Tadashi, and Kazuma Shimomoto. "Bertini theorem for normality on local rings in mixed characteristic (applications to characteristic ideals)." Nagoya Mathematical Journal 218 (June 2015): 125–73. http://dx.doi.org/10.1215/00277630-2891620.

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AbstractIn this article, we prove a strong version of the local Bertini theorem for normality on local rings in mixed characteristic. The main result asserts that a generic hyperplane section of a normal, Cohen–Macaulay, and complete local domain of dimension at least 3 is normal. Applications include the study of characteristic ideals attached to torsion modules over normal domains, which is fundamental in the study of Euler system theory, Iwasawa's main conjectures, and the deformation theory of Galois representations.
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Sun, Liping, Wende Liu, Xiaocheng Gao, and Boying Wu. "Restricted Envelopes of Lie Superalgebras." Algebra Colloquium 22, no. 02 (April 15, 2015): 309–20. http://dx.doi.org/10.1142/s1005386715000279.

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Certain important results concerning p-envelopes of modular Lie algebras are generalized to the super-case. In particular, any p-envelope of the Lie algebra of a Lie superalgebra can be naturally extended to a restricted envelope of the Lie superalgebra. As an application, a theorem on the representations of Lie superalgebras is given, which is a super-version of Iwasawa's theorem in Lie algebra case. As an example, the minimal restricted envelopes are computed for three series of modular Lie superalgebras of Cartan type.
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Dissertations / Theses on the topic "Iwasawa's"

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Baccari, Kevin J. "Homomorphic Images And Related Topics." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/224.

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We will explore progenitors extensively throughout this project. The progenitor, developed by Robert T Curtis, is a special type of infinite group formed by a semi-direct product of a free group m*n and a transitive permutation group of degree n. Since progenitors are infinite, we add necessary relations to produce finite homomorphic images. Curtis found that any non-abelian simple group is a homomorphic image of a progenitor of the form 2*n: N. In particular, we will investigate progenitors that generate two of the Mathieu sporadic groups, M11 and M11, as well as some classical groups. We will prove their existences a variety of different ways, including the process of double coset enumeration, Iwasawa's Lemma, and linear fractional mappings. We will also investigate the various techniques of finding finite images and their corresponding isomorphism types.
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Lamp, Leonard B. "SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/222.

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The goal of this thesis is to show constructions of some of the sporadic groups such as the Mathieu group, M12, J1, Projective Special Linear groups, PSL(2,8), and PSL(2,11), Unitary group U(3,3) and many other non-abelian simple groups. Our purpose is to find all simple non-abelian groups as homomorphic images of permutation or monomial progenitors, as well grasping a deep understanding of group theory and extension theory to determine groups up to isomorphisms. The progenitor, developed by Robert T. Curtis, is a semi-direct product of the following form: P≅2*n: N = {πw | π ∈ N, w a reduced word in the ti} where 2*n denotes a free product of n copies of the cyclic group of order 2 generated by involutions ti for 1 ≤ i≤ n; and N is a transitive permutation group of degree n which acts on the free product by permuting the involuntary generators by conjugation. Thus we develop methods for factoring by a suitable any number of relations in the hope of finding all non-abelian simple groups, and in particular one of the 26 Sporadic simple groups. Then the algorithm for double coset enumeration together with the first isomorphic theorem aids us in proving the homomorphic image of the group we have constructed. After being presented with a group G, we then compute the composition series to solve extension problems. Given a composition such as G = G0 ≥ G1 ≥ ….. ≥ Gn-1 ≥ Gn = 1 and the corresponding factor groups G0/G1 = Q1,…,Gn-2/Gn-1 = Qn-1,Gn-1/Gn = Qn. We note that G1 = 1, implying Gn-1 = Qn. As we move through the next composition factor we see that Gn-2/Qn = Qn-1, so that Gn-2 is an extension of Qn-1 by Qn. Following this procedure we can recapture G from the products of Qi and thus solve the extension problem. The Jordan-Holder theorem then allows us to develop a process to analyze all finite groups if we knew all finite simple groups and could solve their extension problem, hence arriving at the isomorphism type of the group. We will present how we solve extensions problems while our main focus will lie on extensions that will include the following: semi-direct products, direct products, central extensions and mixed extensions.Lastly, we will discuss Iwasawa's Lemma and how double coset enumeration aids us in showing the simplicity of some of our groups.
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Hahn, Rebekah D. "K(1)-local Iwasawa theory /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/5736.

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Ochi, Yoshihiro. "Iwasawa modules via homotopy theory." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624327.

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Tang, Shu-Leung. "Iwasawa invariants over quadratic fields /." The Ohio State University, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487844105976629.

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Buyukboduk, Kazim. "Kolyvagin Systems over an Iwasawa algebra /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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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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Oh, Jangheon. "On Zeta Functions and Iwasawa Modules /." The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487930304689598.

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Venjakob, Otmar. "Iwasawa theory of p-adic Lie extensions." [S.l. : s.n.], 2001. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB9590147.

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Venjakob, Otmar. "Iwasawa theory of r-adic [rho-adic] Lie extensions." [S.l.] : [s.n.], 2000. http://deposit.ddb.de/cgi-bin/dokserv?idn=961907630.

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Books on the topic "Iwasawa's"

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Bouganis, Thanasis, and Otmar Venjakob, eds. Iwasawa Theory 2012. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-55245-8.

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1927-, Satake Ichirō, ed. Kenkichi Iwasawa collected papers. Tokyo: Springer, 2001.

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Iwasawa, Kenkichi. Kenkichi Iwasawa collected papers. Tokyo: Springer, 2001.

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Satake, Ichiro, Genjiro Fujisaki, Kazuya Kato, Masato Kurihara, and Shoichi Nakajima, eds. Kenkichi Iwasawa Collected Papers. Tokyo: Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67947-9.

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Hilbert modular forms and Iwasawa theory. Oxford: Clarendon, 2006.

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Guwahati Workshop on Iwasawa Theory of Totally Real Fields (2008 Indian Institute of Technology, Guwahati). Guwahati Workshop on Iwasawa Theory of Totally Real Fields. Edited by Coates, J., editor of compilation and Ramanujan Mathematical Society. Mysore: Ramanujan Mathematical Society, 2010.

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Iwasawa theory, projective modules, and modular representations. Providence, R.I: American Mathematical Society, 2010.

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Non-abelian fundamental groups in Iwasawa theory. Cambridge: Cambridge University Press, 2011.

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Loeffler, David, and Sarah Livia Zerbes, eds. Elliptic Curves, Modular Forms and Iwasawa Theory. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45032-2.

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Coates, John, Minhyong Kim, Florian Pop, Mohamed Saidi, and Peter Schneider, eds. Non-abelian Fundamental Groups and Iwasawa Theory. Cambridge: Cambridge University Press, 2009. http://dx.doi.org/10.1017/cbo9780511984440.

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Book chapters on the topic "Iwasawa's"

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Neukirch, Jürgen, Alexander Schmidt, and Kay Wingberg. "Iwasawa Modules." In Grundlehren der mathematischen Wissenschaften, 267–333. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-37889-1_5.

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Washington, Lawrence C. "Iwasawa’s Theory of ℤ-extensions." In Graduate Texts in Mathematics, 264–320. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1934-7_13.

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Fernández, Marisa, and Alfred Gray. "The Iwasawa manifold." In Lecture Notes in Mathematics, 157–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0076628.

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Bump, Daniel. "The Iwasawa Decomposition." In Lie Groups, 197–204. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4757-4094-3_29.

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Sujatha, R. "Elliptic Curves and Iwasawa’s µ = 0 Conjecture." In Quadratic Forms, Linear Algebraic Groups, and Cohomology, 125–35. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6211-9_7.

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Washington, Lawrence C. "Iwasawa’s Construction of p-adic L-functions." In Graduate Texts in Mathematics, 113–42. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1934-7_7.

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Jorgenson, Jay, and Serge Lang. "Iwasawa Decomposition and Positivity." In Springer Monographs in Mathematics, 1–32. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4684-9302-3_1.

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Lang, Serge. "Measures and Iwasawa Power Series." In Graduate Texts in Mathematics, 244–68. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4612-0987-4_10.

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Lang, Serge. "Iwasawa Theory of Local Units." In Graduate Texts in Mathematics, 166–89. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4612-0987-4_7.

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Greenberg, Ralph. "Iwasawa theory for elliptic curves." In Lecture Notes in Mathematics, 51–144. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0093453.

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Conference papers on the topic "Iwasawa's"

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Misra, Aalok. "Uplifting the Iwasawa." In PARTICLES, STRINGS, AND COSMOLOGY: 11th International Symposium on Particles, Strings, and Cosmology; PASCOS 2005. AIP, 2005. http://dx.doi.org/10.1063/1.2149733.

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Jian, Bing, and Baba C. Vemuri. "Metric Learning Using Iwasawa Decomposition." In 2007 IEEE 11th International Conference on Computer Vision. IEEE, 2007. http://dx.doi.org/10.1109/iccv.2007.4408846.

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Lenz, Reiner, Rika Mochizuki, and Jinhui Chao. "Iwasawa Decomposition and Computational Riemannian Geometry." In 2010 20th International Conference on Pattern Recognition (ICPR). IEEE, 2010. http://dx.doi.org/10.1109/icpr.2010.1086.

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Kissel, Glen J. "Analyzing light localization using Iwasawa-canonical transfer matrices." In Integrated Optoelectronic Devices 2008, edited by Ali Adibi, Shawn-Yu Lin, and Axel Scherer. SPIE, 2008. http://dx.doi.org/10.1117/12.763886.

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Lu, Shengnan, Xilun Ding, and Gregory S. Chirikjian. "Rotations in a Non-Orthogonal Frame." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85862.

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This paper is concerned with describing the space of matrices that describe rotations in non-orthogonal coordinates. In scenarios such as in crystallography, conformational analysis of polymers, and in the study of deployable mechanisms and rigid origami, non-orthogonal reference frames are natural. For example, non-orthogonal vectors in the direction of atomic bonds in a molecule, the lattice coordinates of a crystal, or the directions of links in a mechanism are intrinsic. In these cases it is awkward to impose an artificial orthonormal reference frame rather than choosing one that is defined by the geometry of the object being studied. With these applications in mind, we fully characterize the space of all possible non-orthogonal rotations. We find that in the 2D case, this space is a three-dimensional subset of the special linear group, SL(2, R), which is itself a three-dimensional Lie group. In the 3D case we find that the space of nonorthogonal rotations is a seven-dimensional subspace of SL(3, R), which is an eight-dimensional Lie group. In the 2D case we use the Iwasawa decomposition to fully characterize the solution. In the 3D case we parameterize this seven-dimensional space by conjugating elements of the rotation group SO(3) by elements of a discrete family of of four-parameter subgroups of GL(3, R), and using this we derive an inversion formula to extract classical orthogonal rotations from those expressed in non-orthogonal coordinates.
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