[geometry-ml:01165] Seminar at IPMU on 11/16 Mieda, 11/17 Abe

[Satoshi Kondo]

Dear colleagues:

We announce the following seminar at IPMU
(the Institute for the Physics and Mathematics of the Universe).

Regards,

Satoshi Kondo (IPMU)
http://ipmu.jp/
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Speaker: Yoichi Mieda (Kyushu U.)
Time: Nov. 16 (Tue), 15:30-17:00
Place: Seminar room A
Title: Lefschetz trace formula and the l-adic cohomology of the
Rapoport-Zink spaces
Abastract:
(Part 1) The Rapoport-Zink spaces are generalizations of the Lubin-Tate space,
which gives a geometric realization of the local Langlands correspondence
for GL(n) and the local Jacquet-Langlands correspondence. In the first part,
I will recall what is expected for the l-adic cohomology of the Rapoport-Zink
spaces.  I will also explain a method of calculating them by using Lefschetz
trace formula for rigid spaces.
(Part 2)  First I will discuss on the Lefschetz trace formula for rigid spaces
which are not necessarily proper over a non-archimedean field.  Next I will
give the precise definition of the Rapoport-Zink space for GSp(4) and explain
how our trace formula can be used to calculate the l-adic cohomology of it.
---------------------
Speaker: Tomoyuki Abe (U. Tokyo)
Time: Nov. 17 (Wed) 15:30-17:00
Place: Lecture Hall
Title: The theory of arithmetic D-modules and characteristic cycles
Abstract:
In this talk, I want to introduce the characteristic cycles of
arithmetic D-modules
due to P. Berthelot, and talk about my recent results concerning this theory.
The theory of D-modules was originated in Sato, Kashiwara, and others' research
on integrable linear differential equation. A surprising thing is that
"analysis" (which is
"difficult" in some sense) can be interpreted by means of algebraic methods
 (namely cohomology theory, which is more or less easier).
I will discuss on the attempt to import this theory in the setting of
"arrithmetic",
and what we can do with this new tool.

After talking about the global picture of the theory, I will briefly
review of the
 theory of Berthelot, and we will see the relation between characteristic
cycles and Swan conductors.  Then I will introduce the ring of
microdifferential
operators for the further analysis on characteristic cycles.
We will conclude this talk by pointing out future applications of the theory,
namely the theory of local Fourier transform, and conjectural
stationary phase formula.
============
You can check the location from
http://www.ipmu.jp/access/img/KashiwaCampusMap.png
The schedule of the seminar can be checked from
http://db.ipmu.jp/seminar/