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Let $p$ be a prime number, $ℚ_{p}$ the field of $p$ -adic numbers and $ℂ_{p}$ the completion of the algebraic closure of $ℚ_{p}$ . In this paper we obtain a representation theorem for rigid analytic functions on $𝐏^{1} (ℂ_{p}) ∖ C (t, ϵ)$ which are equivariant with respect to the Galois group $G = G a l_{c o n t} (ℂ_{p} / ℚ_{p})$ , where $t$ is a lipschitzian element of $ℂ_{p}$ and $C (t, ϵ)$ denotes the $ϵ$ -neighborhood of the $G$ -orbit of $t$ .

A Rigid Analytic Version of M. Artin's Theorem on Analytic Equations.

Siegfried Bosch (1981)

Mathematische Annalen

A septic with 99 real nodes

Oliver Labs (2006)

Rendiconti del Seminario Matematico della Università di Padova

A Short Proof of the Rydakov-Safarevic Theorem.

William E. Lang, Niels O. Nygaard (1980)

Mathematische Annalen

A Siegel modular 3-fold that is a Picard modular 3-fold

Bruce Hunt (1990)

Compositio Mathematica

A souped-up version of Pardini's theorem and its application to funny curves

Masaaki Homma (1989)

Compositio Mathematica

A System of Free Generators for the Universal even Ordinary Z(2) Distribution on Q2k-Z2k .

Dan Kubert (1976)

Mathematische Annalen

A vanishing theorem on arithmetic surfaces.

C. Soulé (1994)

Inventiones mathematicae

A weak Néron model with applications to $p$ -adic dynamical systems

Liang-Chung Hsia (1996)

Compositio Mathematica

Abelian surfaces and jacobian varieties over finite fields

Hans-Georg Rück (1990)

Compositio Mathematica

Abelian varieties in $W_{d}^{r} (C)$ and points of bounded degree on algebraic curves

Olivier Debarre, Rachid Fahlaoui (1993)

Compositio Mathematica

Abelian Varieties, l-adic Representations and Lie Algebras.

Yu. G. Zarhin (1979)

Inventiones mathematicae

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.

Abelian varieties over finite fields with a specified characteristic polynomial modulo $ℓ$

Joshua Holden (2004)

Journal de Théorie des Nombres de Bordeaux

We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial $P (T)$ modulo $ℓ$ . As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order $ℓ$ .

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