Finiteness of Crystalline Cohomology of Higher Level

TL;DR

This paper proves the finiteness of crystalline cohomology at higher levels using a novel higher de Rham complex and a Poincaré lemma, advancing understanding in algebraic geometry.

Contribution

Introduces a higher de Rham complex and Poincaré lemma to establish the finiteness of crystalline cohomology at higher levels.

Findings

Crystalline cohomology of higher level is finite.

Development of a higher de Rham complex.

Establishment of a Poincaré lemma for the complex.

Abstract

We prove the finiteness of crystalline cohomology of higher level. An important ingredient is a "higher de Rham complex" and a kind of Poincar\'e lemma for it.