Algebraic de Rham cohomology and the Degeneration of the Hodge spectral sequence

In this post we will discuss various properties of the algebraic de Rham cohomology of a variety . We will focus, in particular, on various aspects of when the Hodge-to-de Rham spectral sequence on the first page, the most interesting case of which happens in positive characteristic.

An invitation to p-adic Hodge theory, or: How i learned to stop worrying and love period rings

This is the rough outline of a talk I recently gave at the Berkeley Student Algebraic Geometry Seminar on the progression of ideas that might lead one to define the Hodge-Tate decomposition.