Work

The Hilbert symbol in the Hodge standard conjecture

Year: 2025

Type: article

Abstract: We study the Hodge standard conjecture for varieties over finite fields admitting a CM lifting, such as abelian varieties or products of K3 surfaces. For those varieties we show that the signature predicted by the conjecture holds true modulo 4 . This amounts to determining the discriminant and the Hilbert symbol of the intersection product. The first is obtained by \ell -adic arguments whereas the second needs a careful computation in p -adic Hodge theory.

Source: Commentarii Mathematici Helvetici

DOI: 10.4171/cmh/591

Authors: Giuseppe Ancona, Adriano Marmora

Institutions: Centre National de la Recherche Scientifique, Université de Strasbourg

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Award: Algebraic cycles and periods