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1981•Mathematics of the USSR-IzvestiyaRequires access

POINTS OF FINITE ORDER ON AN ABELIAN VARIETY

Fedor Bogomolov

Open publisher page 40 citations

Abstract

In this paper it is shown that the image of the Galois group under an -adic representation in the Tate module of an abelian variety has an algebraic Lie algebra which contains the scalar matrices as a subalgebra (Serre's conjecture). This paper also proves the finiteness of the intersection of a subgroup of an abelian variety all of whose elements have order equal to a power of a fixed number with a wide class of subvarieties. Bibliography: 13 titles.

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What this paper is about

In this paper it is shown that the image of the Galois group under an -adic representation in the Tate module of an abelian variety has an algebraic Lie algebra which contains the scalar matrices as a subalgebra (Serre's conjecture). This paper also proves the finiteness of the intersection of a subgroup of an abelian variety all of whose elements have order equal to a power of a fixed number with a wide class of subvarieties. Bibliography: 13 titles.

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OpenAlex reports 40 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper it is shown that the image of the Galois group under an -adic representation in the Tate module of an abelian variety has an algebraic Lie algebra which contains the scalar matrices as a subalgebra (Serre's conjecture). This paper also proves the finiteness of the intersection of a subgroup of an abelian variety all of whose elements have order equal to a power of a fixed number with a wide class of subvarieties. Bibliography: 13 titles.

Key concepts: Variety (cybernetics), Order (exchange), Abelian group, Mathematics, Pure mathematics, Business, Statistics, Finance

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