# On infiniteness of integral overconvergent de Rham-Witt cohomology modulo torsion

## TL;DR

This paper provides examples of smooth varieties in positive characteristic where the first integral overconvergent de Rham-Witt cohomology modulo torsion is not finitely generated, challenging assumptions about its structure.

## Contribution

It demonstrates that the first integral overconvergent de Rham-Witt cohomology modulo torsion can be infinitely generated, providing new insights into its algebraic properties.

## Key findings

- First integral overconvergent de Rham-Witt cohomology modulo torsion is not finitely generated in certain cases.
- Examples of smooth varieties with non-finitely generated cohomology.
- Challenges previous expectations of finiteness in this cohomology theory.

## Abstract

In this article, we give examples of smooth varieties of positive characteristic whose first integral overconvergent de Rham-Witt cohomology modulo torsion is not finitely generated over the Witt ring of the base field.