Arbitrarily large jumps in the de Rham and Hodge cohomology of families in characteristic $p$

Fuente: arXiv
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Autor principal: Kothari, Casimir
Formato: Preprint
Publicado: 2023
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author Kothari, Casimir
author_facet Kothari, Casimir
contents We construct smooth projective families of algebraic varieties in characteristic $p$ such that the dimensions of the de Rham and Hodge cohomology groups of the fibers can be made to jump by an arbitrarily large amount. To do this, we first construct an example using the classifying stack of a finite flat group scheme which degenerates $\mathbb{Z}/p^2\mathbb{Z}$ to $α_p \oplus α_p$. Along the way, we give a self-contained exposition of the construction of Godeaux--Serre varieties.
format Preprint
id arxiv_https___arxiv_org_abs_2304_07628
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Arbitrarily large jumps in the de Rham and Hodge cohomology of families in characteristic $p$
Kothari, Casimir
Algebraic Geometry
Number Theory
14D10 (Primary) 14F40, 14L15 (Secondary)
We construct smooth projective families of algebraic varieties in characteristic $p$ such that the dimensions of the de Rham and Hodge cohomology groups of the fibers can be made to jump by an arbitrarily large amount. To do this, we first construct an example using the classifying stack of a finite flat group scheme which degenerates $\mathbb{Z}/p^2\mathbb{Z}$ to $α_p \oplus α_p$. Along the way, we give a self-contained exposition of the construction of Godeaux--Serre varieties.
title Arbitrarily large jumps in the de Rham and Hodge cohomology of families in characteristic $p$
topic Algebraic Geometry
Number Theory
14D10 (Primary) 14F40, 14L15 (Secondary)
url https://arxiv.org/abs/2304.07628