The Hilbert symbol in the Hodge standard conjecture
Algebraic Geometry
2025-01-22 v3 Number Theory
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 . This amounts to determining the discriminant and the Hilbert symbol of the intersection product. The first is obtained by -adic arguments whereas the second needs a careful computation in -adic Hodge theory.
Cite
@article{arxiv.2210.14001,
title = {The Hilbert symbol in the Hodge standard conjecture},
author = {Giuseppe Ancona and Adriano Marmora},
journal= {arXiv preprint arXiv:2210.14001},
year = {2025}
}
Comments
revised version, accepted in Commentarii Mathematici Helvetici; 31 pages, 1 figure