An introduction to isocrystals
An introduction to isocrystals

Linus Hamann, Princeton University
Fine Hall 110
An isocrystal is a type of linear algebraic datum that describes various objects arising in arithmetic algebraic geometry. On the one hand, they have a relatively concrete description as vector spaces
over a field together with some special endomorphisms. This makes them very amenable to computation. On the other, they are linked to very important structures in Arithmetic Geometry such as pdivisible groups and the crystalline cohomology of algebraic varieties. This dual nature makes them indispensable tools for tackling many problems. In this talk, we will define the category of isocrystals over a field of characeristic p, explain its basic properties, and give some
applications.