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Littérature scientifique sur le sujet « Abelian varietie »

Auteur : Grafiati

Publié le 9 mars 2023

Mis à jour le 10 mars 2023

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Articles de revues sur le sujet "Abelian varietie"

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Zhao, Heer. "Degenerating abelian varieties via log abelian varieties." Asian Journal of Mathematics 22, no. 5 (2018): 811–40. http://dx.doi.org/10.4310/ajm.2018.v22.n5.a2.

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Silverberg, Alice. "abelian varieties." Duke Mathematical Journal 56, no. 1 (1988): 41–46. http://dx.doi.org/10.1215/s0012-7094-88-05603-7.

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Yu, Chia-Fu. "Abelian varieties over finite fields as basic abelian varieties." Forum Mathematicum 29, no. 2 (2017): 489–500. http://dx.doi.org/10.1515/forum-2014-0141.

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AbstractIn this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic ${p>0}$ is isogenous to another one defined over a finite field. We also show that the category of abelian varieties over finite fields up to isogeny can be embedded into the category of basic abelian varieties with suitable endomorphism structures. Using this connection, we derive a new mass formula for a finite orbit of polarized abelian surfaces over a finite field.

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Kajiwara, Takeshi, Kazuya Kato, and Chikara Nakayama. "Logarithmic Abelian Varieties." Nagoya Mathematical Journal 189 (2008): 63–138. http://dx.doi.org/10.1017/s002776300000951x.

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AbstractWe develop the algebraic theory of log abelian varieties. This is Part II of our series of papers on log abelian varieties, and is an algebraic counterpart of the previous Part I ([6]), where we developed the analytic theory of log abelian varieties.

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Yamaki, Kazuhiko. "Trace of abelian varieties over function fields and the geometric Bogomolov conjecture." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 741 (2018): 133–59. http://dx.doi.org/10.1515/crelle-2015-0086.

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Abstract We prove that the geometric Bogomolov conjecture for any abelian varieties is reduced to that for nowhere degenerate abelian varieties with trivial trace. In particular, the geometric Bogomolov conjecture holds for abelian varieties whose maximal nowhere degenerate abelian subvariety is isogenous to a constant abelian variety. To prove the results, we investigate closed subvarieties of abelian schemes over constant varieties, where constant varieties are varieties over a function field which can be defined over the constant field of the function field.

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Totaro, Burt. "Pseudo-abelian varieties." Annales scientifiques de l'École normale supérieure 46, no. 5 (2013): 693–721. http://dx.doi.org/10.24033/asens.2199.

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Ji, Shanyu. "on abelian varieties." Duke Mathematical Journal 58, no. 3 (1989): 657–67. http://dx.doi.org/10.1215/s0012-7094-89-05831-6.

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Bosch, Siegfried, and Werner Lütkebohmert. "Degenerating abelian varieties." Topology 30, no. 4 (1991): 653–98. http://dx.doi.org/10.1016/0040-9383(91)90045-6.

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Archinard, Natália. "Hypergeometric Abelian Varieties." Canadian Journal of Mathematics 55, no. 5 (2003): 897–932. http://dx.doi.org/10.4153/cjm-2003-037-4.

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AbstractIn this paper, we construct abelian varieties associated to Gauss’ and Appell–Lauricella hypergeometric series. Abelian varieties of this kind and the algebraic curves we define to construct them were considered by several authors in settings ranging from monodromy groups (Deligne, Mostow), exceptional sets (Cohen, Wolfart, Wüstholz), modular embeddings (Cohen, Wolfart) to CM-type (Cohen, Shiga, Wolfart) and modularity (Darmon). Our contribution is to provide a complete, explicit and self-contained geometric construction.

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Chai, Ching-Li, and Frans Oort. "Hypersymmetric Abelian Varieties." Pure and Applied Mathematics Quarterly 2, no. 1 (2006): 1–27. http://dx.doi.org/10.4310/pamq.2006.v2.n1.a2.

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Thèses sur le sujet "Abelian varietie"

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TAMBORINI, CAROLINA. "On totally geodesic subvarieties in the Torelli locus and their uniformizing symmetric spaces." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/371476.

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Oggetto di questa tesi sono le sottovarietà totalmente geodetiche dello spazio dei moduli A_g di varietà abeliane principalmente polarizzate e la loro relazione con il luogo di Torelli. Questo è definito come la chiusura in A_g dell'immagine dello spazio dei moduli M_g di curve algebriche complesse lisce di genere g tramite la mappa di Torelli j: M_g-->A_g. Lo spazio dei moduli A_g è un quoziente dello spazio di Siegel, che è uno spazio simmetrico. Una sottovarietà algebrica di A_g è totalmente geodetica se è l'immagine, tramite la naturale mappa di proiezione, di una qualche sottovarietà tota

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歐偉民 and Wai-man Au. "Families of polarized abelian varieties." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31214897.

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Lemos, Pedro. "Residual representations of Abelian varieties." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/94788/.

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This thesis is divided in two parts, corresponding to two papers in which I collaborated during the course of my PhD studies. Both of these parts are concerned with the question of surjectivity of residual Galois representations arising from abelian varieties defined over Q. At the start of each chapter, a full introduction to the topic covered is provided.

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Fhlathuin, Brid ni. "Mahler's measure on Abelian varieties." Thesis, University of East Anglia, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296951.

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This thesis is a study of the integration of proximity functions over certain compact groups. Mean values are found of the ultrametric valuation of certain rational functions associated with a divisor on an abelian variety, and it is shown how these may be expressed in terms of an integral, thus finding the analogue, for an abelian variety, of Mahler's definition of the measure of a polynomial. These integrals are shown to arise in a manner which mimics classical Riemann sums, and their relation with the global canonical height is investigated. It is shown that the measure is a rational multip

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Au, Wai-man. "Families of polarized abelian varieties /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B19471117.

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Young, Ian David. "Symmetric squares of modular Abelian varieties." Thesis, University of Sheffield, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.500087.

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Giangreco, Maidana Alejandro José. "Cyclic abelian varieties over finite fields." Thesis, Aix-Marseille, 2019. http://www.theses.fr/2019AIXM0316.

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L'ensemble A(k) des points rationnels d'une variété abélienne A définie sur un corps fini k forme un groupe abélien fini. Ce groupe convient pour des multiples applications, et sa structure est très importante. Connaître les possibles structures de groupe des A(k) et quelques statistiques est donc fondamental. Dans cette thèse, on s'intéresse aux "variétés cycliques", i.e. variétés abéliennes définies sur des corps finis avec groupe des points rationnels cyclique.Les isogénies nous donnent une classification plus grossière que celle donnée par les classes d'isomorphisme des variétés abéliennes

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Joyce, Adam Jack. "The Manin constants of modular abelian varieties." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.440468.

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Lahoz, Vilalta Marti. "Theta-duality in abelian varieties and the bicanonical map of irregular varieties." Doctoral thesis, Universitat Politècnica de Catalunya, 2010. http://hdl.handle.net/10803/77898.

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The first goal of this Thesis is to contribute to the study of principally polarized abelian varieties (ppav), especially to the Schottky and the Torelli problems. Ppav admit a duality theory analogous to that of projective spaces, where the role played by hyperplanes in projective spaces is played by divisors representing the principal polarization. Thus, given a subvariety Y of a ppav, we can define its thetadual T(Y) as the set of divisors representing the principal polarization that contain this subvariety. This set admits a natural schematic structure (as defined by Pareschi and Popa

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Borowka, Pawel. "Non-simple abelian varieties and (1,3) Theta divisors." Thesis, University of Bath, 2012. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.564009.

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This thesis studies non-simple Jacobians and non-simple abelian varieties. The moti- vation of the study is a construction which gives a distinguished genus 4 curve in the linear system of a (1, 3)-polarised surface. The main theorem characterises such curves as hyperelliptic genus 4 curves whose Jacobian contains a (1, 3)-polarised surface. This leads to investigating the locus of non-simple principally polarised abelian g- folds. The main theorem of this part shows that the irreducible components of this locus are Is~, defined as the locus of principally polarised g-folds having an abelian s

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Livres sur le sujet "Abelian varietie"

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Barth, Wolf, Klaus Hulek, and Herbert Lange, eds. Abelian Varieties. DE GRUYTER, 1995. http://dx.doi.org/10.1515/9783110889437.

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Lange, Herbert. Complex Abelian varieties. Springer, 1992.

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Lange, Herbert, and Christina Birkenhake. Complex Abelian Varieties. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02788-2.

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Birkenhake, Christina, and Herbert Lange. Complex Abelian Varieties. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06307-1.

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H, Lange. Complex Abelian varieties. Springer-Verlag, 1992.

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1943-, Lange H., and Lange H. 1943-, eds. Complex Abelian varieties. 2nd ed. Springer, 2004.

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Faber, Carel, Gerard van der Geer, and Frans Oort, eds. Moduli of Abelian Varieties. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8303-0.

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Faltings, Gerd, and Ching-Li Chai. Degeneration of Abelian Varieties. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-662-02632-8.

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Adler, Allan, and Sundararaman Ramanan. Moduli of Abelian Varieties. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0093659.

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Alexeev, Valery, Arnaud Beauville, C. Herbert Clemens, and Elham Izadi, eds. Curves and Abelian Varieties. American Mathematical Society, 2008. http://dx.doi.org/10.1090/conm/465.

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Chapitres de livres sur le sujet "Abelian varietie"

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Gamkrelidze, R. V. "Abelian Varieties." In Encyclopaedia of Mathematical Sciences. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58227-1_3.

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Fresnel, Jean, and Marius van der Put. "Abelian Varieties." In Rigid Analytic Geometry and Its Applications. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0041-3_6.

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Milne, J. S. "Abelian Varieties." In Arithmetic Geometry. Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4613-8655-1_5.

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Hurt, Norman E. "Abelian Varieties." In Many Rational Points. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0251-5_1.

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Birkenhake, Christina, and Herbert Lange. "Abelian Varieties." In Complex Abelian Varieties. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06307-1_6.

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Lange, Herbert, and Christina Birkenhake. "Abelian Varieties." In Complex Abelian Varieties. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02788-2_6.

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Birkenhake, Christina, and Herbert Lange. "Jacobian Varieties." In Complex Abelian Varieties. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06307-1_13.

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Birkenhake, Christina, and Herbert Lange. "Prym Varieties." In Complex Abelian Varieties. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06307-1_14.

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Lange, Herbert, and Christina Birkenhake. "Jacobian Varieties." In Complex Abelian Varieties. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02788-2_13.

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Lange, Herbert, and Christina Birkenhake. "Prym Varieties." In Complex Abelian Varieties. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02788-2_14.

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Actes de conférences sur le sujet "Abelian varietie"

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Blake, Ian F. "Abelian varieties in coding and cryptography." In 2010 IEEE Information Theory Workshop (ITW 2010). IEEE, 2010. http://dx.doi.org/10.1109/cig.2010.5592929.

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Lawson, Tyler. "An overview of abelian varieties in homotopy theory." In New topological contexts for Galois theory and algebraic geometry. Mathematical Sciences Publishers, 2009. http://dx.doi.org/10.2140/gtm.2009.16.179.

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POLÁK, L. "LITERAL VARIETIES AND PSEUDOVARIETIES OF HOMOMORPHISMS ONTO ABELIAN GROUPS." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708700_0018.

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