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Semistable reduction and torsion subgroups of abelian varieties

Alice Silverberg, Yuri G. Zarhin (1995)

Annales de l'institut Fourier

The main result of this paper implies that if an abelian variety over a field $F$ has a maximal isotropic subgroup of $n$ -torsion points all of which are defined over $F$ , and $n \geq 5$ , then the abelian variety has semistable reduction away from $n$ . This result can be viewed as an extension of Raynaud’s theorem that if an abelian variety and all its $n$ -torsion points are defined over a field $F$ and $n \geq 3$ , then the abelian variety has semistable reduction away from $n$ . We also give information about the Néron models...

Série de Poincaré pour certaines courbes

Roberto Sánchez Peregrino (1991)

Rendiconti del Seminario Matematico della Università di Padova

Sieve methods for varieties over finite fields and arithmetic schemes

Bjorn Poonen (2007)

Journal de Théorie des Nombres de Bordeaux

Classical sieve methods of analytic number theory have recently been adapted to a geometric setting. In the new setting, the primes are replaced by the closed points of a variety over a finite field or more generally of a scheme of finite type over $ℤ$ . We will present the method and some of the surprising results that have been proved using it. For instance, the probability that a plane curve over $𝔽_{2}$ is smooth is asymptotically $21 / 64$ as its degree tends to infinity. Much of this paper is an exposition...

Singularities of Quotients by Vector Fields in Characteristic p.

Luchezar L. Avramov, Annetta G. Aramova (1985/1986)

Mathematische Annalen

Smooth degeneration of complete intersection curves in positive characteristc.

Mohan N. Kumar (1991)

Inventiones mathematicae

Some Consequences of the Riemann Hypothesis for Varieties over Finite Fields.

Nicholas M. Katz, William Messing (1974)

Inventiones mathematicae

Some elliptic function identities

J. Cassels (1971)

Acta Arithmetica

Some estimates from étale cohomology.

J.S. Milne (1981)

Journal für die reine und angewandte Mathematik

Some p-adic Galois Representations for Curves in Characteristic p.

Robert C. Valentini (1986)

Mathematische Zeitschrift

Some remarks on plane curves over fields of finite characteristic

Rita Pardini (1986)

Compositio Mathematica

Stable Vector Bundles on Projective Spaces in Char p > 0.

Lawrence Ein (1980)

Mathematische Annalen

Supersingular curves of genus two and class numbers

Tomoyoshi Ibukiyama, Toshiyuki Katsura, Frans Oort (1986)

Compositio Mathematica

Sur la multiplication complexe dans les fonctions elliptiques et, en particulier, sur la multiplication par $\sqrt{- 23}$

G.-H. Halphen (1889)

Journal de Mathématiques Pures et Appliquées

Sur la transcendance de la série formelle Π

Jean-Paul Allouche (1990)

Journal de théorie des nombres de Bordeaux

En utilisant le théorème de Christol, Kamae, Mendès France et Rauzy, nous donnons une démonstration élémentaire de la transcendance de la série formelle $Π$ ainsi que d’autres séries formelles à coefficients dans un corps fini.

Sur le plongement projectif des surfaces définies sur un corps de base fini

Marco Fontana (1975)

Compositio Mathematica

Sur le Topos infinitésimal $p$ -adique d’un schéma lisse I

Alberto Arabia, Zoghman Mebkhout (2010)

Annales de l’institut Fourier

Afin de disposer des opérations cohomologiques aussi souples que possible pour la cohomologie de de Rham $p$ -adique, le but principal de ce mémoire est de résoudre intrinsèquement du point de vue cohomologique le problème des relèvements des schémas lisses et de leurs morphismes de la caractéristique $p > 0$ à la caractéristique nulle ce qui a été l’une des difficultés centrales de la théorie de la cohomologie de de Rham des schémas algébriques en caractéristique positive depuis le début. Nous montrons...

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