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2006•Pure and Applied Mathematics QuarterlyOpen access

Eigenvalues of Frobenius and Hodge Numbers

Mark Kisin, Gus I. Lehrer

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Abstract

We study the connection between Hodge purity of the cohomology of algebraic varieties over fields of different characteristics. Specifically, we study varieties over number fields, whose cohomology in some fixed degree 2i consists entirely of Hodge classes, that is, whose Hodge cohomology in degree 2i is entirely of type

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We study the connection between Hodge purity of the cohomology of algebraic varieties over fields of different characteristics. Specifically, we study varieties over number fields, whose cohomology in some fixed degree 2i consists entirely of Hodge classes, that is, whose Hodge cohomology in degree 2i is entirely of type

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OpenAlex reports 19 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We study the connection between Hodge purity of the cohomology of algebraic varieties over fields of different characteristics. Specifically, we study varieties over number fields, whose cohomology in some fixed degree 2i consists entirely of Hodge classes, that is, whose Hodge cohomology in degree 2i is entirely of type

Key concepts: Mathematics, Hodge theory, Hodge conjecture, Cohomology, Pure mathematics, Hodge structure, Connection (principal bundle), Algebraic variety

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