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37th Autumn School in Algebraic Geometry

##
Topics in characteristic p>0 and p-adic geometry

### Lukecin, Poland, September 7th - September 13th, 2014

**Teachers:**
Bhargav Bhatt (Institute for Advanced Study, Princeton, USA) and Hélène
Esnault (Freie Universität Berlin, Germany)
**Programme:**

The lectures will focus on two related topics: p-adic Hodge theory (B.B.)
and D-modules in positive characteristic and deformations of algebraic cycles (H.E.).

Bhargav Bhatt: *p-adic Hodge theory and applications.*

The cotangent complex.
The derived de Rham complex.
The h-topology and de Jong's alterations.
Some aspects of Fontaine's p-adic Hodge theory.
Comparison theorems, following Beilinson's approach.
Hélène Esnault: * D-modules in positive characteristic and
deformations of algebraic cycles.*

Category of flat connections in characteristic 0.
Analogs over a perfect field k of characteristic p>0:
category of O-coherent D-modules (k-linear category)
and category of isocrystals (K-linear category, K=Frac W(k), W(k)=Witt
vectors).
Relations to the étale fundamental group.
Adic deformations of algebraic cycles (p-adic, equal characteristic 0
and p).
WARNING:
Teachers will cover the above material only if time permits.
It is possible that they will select some of the topics listed
and glide away of the remaining ones.

**Prerequisites:** Basic knowledge of algebraic geometry.

**Organizers:** Agnieszka Bodzenta, Hélène Esnault and Adrian Langer

The school will take place in a University of Warsaw pension in Lukecin
(look here for more
information), on Western part of Polish Baltic sea shore (see a
map). The accommodation (full board, double room) will cost about
160 zloty (PLN) a day (1 Euro is approx. 4.2 PLN). The conference fee
of 60 zloty will apply.
Graduate students, postdocs and other researchers with inadequate support
from their home institutions may apply for accomodation cost waiver.
The conference fee is not covered by the financial support.

The school was financially supported by Berlin Mathematical School,
European Research Council, Warsaw Centre of Mathematics and Computer Science
and Polish National Science Centre (NCN).

Joint photo

September
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