Crystalline cohomology

Abstract: This talk will provide an overview of key concepts in crystalline cohomology. We will begin with Grothendieck's heuristic argument that, because de Rham cohomology is independent of choice of smooth lift, an intrinsic characteristic zero-valued cohomology should exist for schemes in characteristic p. We will then discuss divided power structures and the crystalline site. After stating the key theorems, we will describe a relative setup in which the general theory of topoi plays a more prominent role. We will conclude with sketches of crucial ideas in the comparison isomorphisms, and a glimpse of the relationship between crystals and connections.

algebraic geometrynumber theory

Audience: advanced learners

( slides )

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STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Spring 2024 topic: The contents of Serre, Lectures on the Mordell-Weil theorem

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.

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