Back to Algebraic Geometry Seminar: Fall 2012
Algebraic Geometry Seminar
Date: Tuesday, Nov 20, 2012
Time: 3:30PM - 4:30PM
Location: JTB 120
Bhargav Bhatt
University of Michigan
Title |
p-adic derived de Rham cohomology |
Abstract |
A basic theorem in Hodge theory is the isomorphism between de Rham and Betti cohomology for complex manifolds; this follows directly from the Poincare lemma. The p-adic analogue of this comparison lies deeper, and was the subject of a series of extremely influential conjectures made by Fontaine in the early 80s (which have since been established by various mathematicians). In my talk, I will first discuss the geometric motivation behind Fontaine’s conjectures, and then explain a simple new proof based on general principles in derived algebraic geometry — specifically, derived de Rham cohomology — and some classical geometry with curve fibrations. This work builds on ideas of Beilinson who proved the de Rham comparison conjecture this way. |
Algebraic Geometry