A remark on crystalline cohomology

TL;DR

This paper introduces a novel approach to crystalline cohomology by leveraging the unique lifting of smooth algebras up to coherent homotopy, offering potential new insights in algebraic geometry.

Contribution

It presents a new perspective on crystalline cohomology using homotopical methods, which is a significant departure from traditional techniques.

Findings

Establishes a framework for lifting smooth algebras up to coherent homotopy.

Provides new tools for computing crystalline cohomology.

Suggests potential applications in algebraic geometry and related fields.

Abstract

We propose a new approach to crystalline cohomology based on the observation that one can lift smooth algebras uniquely "up to coherent homotopy."