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1972•Mathematics of the USSR-IzvestiyaRequires access

MINIMAL MODELS OF CURVES OF GENUS 2 AND HOMOMORPHISMS OF ABELIAN VARIETIES DEFINED OVER A FIELD OF FINITE CHARACTERISTIC

A N Paršin

Open publisher page 36 citations

Abstract

In this article, we prove a finiteness theorem for isogenous abelian varieties of dimension 2 defined over a field of algebraic functions of one variable whose characteristic 2. By means of this result, we prove Tate's conjecture on homomorphisms of abelian varieties of dimension 1 defined over the same field.

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What this paper is about

In this article, we prove a finiteness theorem for isogenous abelian varieties of dimension 2 defined over a field of algebraic functions of one variable whose characteristic 2. By means of this result, we prove Tate's conjecture on homomorphisms of abelian varieties of dimension 1 defined over the same field.

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OpenAlex reports 36 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this article, we prove a finiteness theorem for isogenous abelian varieties of dimension 2 defined over a field of algebraic functions of one variable whose characteristic 2. By means of this result, we prove Tate's conjecture on homomorphisms of abelian varieties of dimension 1 defined over the same field.

Key concepts: Homomorphism, Abelian group, Genus, Mathematics, Pure mathematics, Field (mathematics), Finite field, Arithmetic of abelian varieties

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