Time: 10:00 – 12:00, Thursday 4, Friday 5, Tuesday 9, Wednesday 10 and Thursday 11 September, 2014.

Location: VIASM Lecture Hall C2.

Lecturer: Prof. Illusie (Université Paris-Sud)

Abstract:

The purpose of these lectures is to explain Beilinson’s proof of the $p$-adic de Rham comparison theorems using derived de Rham complexes.

(1) Review of the classical Poincaré lemma and Betti-de Rham comparison theorem.

The $p$-adic étale – de Rham comparison theorem : statement, indications on the method of proof.

(2) Review of cotangent complex, derived exterior powers, and derived de Rham complexes. Beilinson’s derived de Rham formula for $B_{dR}$.

(3) Semistable pairs, de Jong’s alterations, Voevodski topology.

(4) Review of log geometry, derived log de Rham complexes. Construction of $\mathcal{A}_{dR}$, Deligne’s Hodge III revisited.

(5) Construction of $\mathcal{A}^{\natural}_{dR}$, Beilinson-Bhatt’s $p$-adic Poincaré lemma. Definition of the comparison map, sketch of proof of the main theorem.

(6) Main points in the proof of the $p$-adic Poincaré lemma.

Reference : A. Beilinson, $p$-adic periods and derived de Rham cohomology, J. of the AMS, 25 (3), 715-738 (2012)

Registration:

Please fill in the registration form below your contact information. Deadline for registration: 30/8/2014.