Hodge and Frobenius colevels of algebraic varieties
Algebraic Geometry
2025-04-23 v3 Number Theory
Abstract
We provide new, improved lower bounds for the Hodge and Frobenius colevels of algebraic varieties (over or over a finite field) in all cohomological degrees. These bounds are expressed in terms of the dimension of the variety and multi-degrees of its defining equations. Our results lead to an enhanced positive answer to a question raised by Esnault and the first author.
Keywords
Cite
@article{arxiv.2309.16290,
title = {Hodge and Frobenius colevels of algebraic varieties},
author = {Daqing Wan and Dingxin Zhang},
journal= {arXiv preprint arXiv:2309.16290},
year = {2025}
}
Comments
25 pages. v3: Corrected the proof of Theorem 2.5. Final version