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A basis for the non-archimedean holomorphic theta functions.

Van Steen, G. (1994)

Bulletin of the Belgian Mathematical Society - Simon Stevin

A generalization of the Chowla-Selberg formula.

Y. Nakkajima, Y. Taguchi (1991)

Journal für die reine und angewandte Mathematik

Abelian surfaces and products of elliptic curves

Marina Rosanna Marchisio (1998)

Bollettino dell'Unione Matematica Italiana

Si dà una nuova e completa dimostrazione del risultato cruciale del metodo di Ruppert che consente di stabilire in maniera effettiva quando una superficie abeliana è isomorfa o isogena a un prodotto di curve ellittiche.

Abelian varieties over fields of finite characteristic

Yuri Zarhin (2014)

Open Mathematics

The aim of this paper is to extend our previous results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.

Bounds on polarizations of abelian varieties over finite fields.

Everett W. Howe (1995)

Journal für die reine und angewandte Mathematik

Classes d'isogénie des variétés abéliennes sur un corps fini

John Tate (1968/1969)

Séminaire Bourbaki

Congruences between cusp forms and the geometry of Jacobians of modular curves.

San Ling (1993)

Mathematische Annalen

Decompositions of an Abelian surface and quadratic forms

Shouhei Ma (2011)

Annales de l’institut Fourier

When a complex Abelian surface can be decomposed into a product of two elliptic curves, how many decompositions does the Abelian surface admit? We provide arithmetic formulae for the number of such decompositions.

Descent via isogeny in dimension 2

E. V. Flynn (1994)

Acta Arithmetica

Endomorphism estimates for abelian varieties.

D.W. Masser, G. Wüstholz (1994)

Mathematische Zeitschrift

Estimating isogenies on elliptic curves.

D.W. Masser, G. Wüstholz (1990)

Inventiones mathematicae

Factorization estimates for abelian varieties

D. W. Masser, G. Wüstholz (1995)

Publications Mathématiques de l'IHÉS

Galois descent and twists of an abelian variety

Masanari Kida (1995)

Acta Arithmetica

La filtration canonique des points de torsion des groupes $p$ -divisibles

Laurent Fargues (2011)

Annales scientifiques de l'École Normale Supérieure

Étant donnés un entier $n \geq 1$ et un groupe de Barsotti-Tate tronqué d’échelon $n$ et de dimension $d$ sur un anneau de valuation d’inégales caractéristiques, nous donnons une borne explicite sur son invariant de Hasse qui implique que sa filtration de Harder-Narasimhan possède un sous-groupe libre de rang $d$ . Lorsque $n = 1$ nous redémontrons également le théorème d’Abbes-Mokrane ([120]) et de Tian ([164]) par des méthodes locales. On applique cela aux familles $p$ -adiques de tels objets et en particulier à certaines...

L'opération de Cartier. Applications

Conjeerveram Srirangachari Seshadri (1958/1959)

Séminaire Claude Chevalley

Minorations de formes linéaires de logarithmes elliptiques

Sinnou David (1995)

Mémoires de la Société Mathématique de France

Motivic decomposition of abelian schemes and the Fourier transform.

Ch. Deninger, Jacob Murre (1991)

Journal für die reine und angewandte Mathematik

On a theorem of Tate

Fedor Bogomolov, Yuri Tschinkel (2008)

Open Mathematics

We study applications of divisibility properties of recurrence sequences to Tate’s theory of abelian varieties over finite fields.

On coverings of simple abelian varieties

Olivier Debarre (2006)

Bulletin de la Société Mathématique de France

To any finite covering $f : Y \to X$ of degree $d$ between smooth complex projective manifolds, one associates a vector bundle $E_{f}$ of rank $d - 1$ on $X$ whose total space contains $Y$ . It is known that $E_{f}$ is ample when $X$ is a projective space ([Lazarsfeld 1980]), a Grassmannian ([Manivel 1997]), or a Lagrangian Grassmannian ([Kim Maniel 1999]). We show an analogous result when $X$ is a simple abelian variety and $f$ does not factor through any nontrivial isogeny $X^{'} \to X$ . This result is obtained by showing that $E_{f}$ is $M$ -regular in the...

Optimal curves differing by a 3-isogeny

Dongho Byeon, Donggeon Yhee (2013)

Acta Arithmetica

Stein and Watkins conjectured that for a certain family of elliptic curves E, the X₀(N)-optimal curve and the X₁(N)-optimal curve of the isogeny class 𝓒 containing E of conductor N differ by a 3-isogeny. In this paper, we show that this conjecture is true.

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