p-adic arithmetic geometry and motives

Workshop on p-adic arithmetic geometry and motives

We will hold a workshop on p-adic arithmetic geometry and motives on the occasion of Professor Bruno Kahn's visit to Japan.

Date:　 January 23-25, 2012
Venue:　 Institute of Mathematics, Tohoku University, Kawai hall.
Access guide: Click here (in English) or here (in Japanese).

Speakers
Tomoyuki Abe (Institute for the Physcs and Mathematics of the Universe)
Masanori Asakura (Hokkaido University)
Olivier Brinon (Université Paris 13)
Naoki Imai (Research Institute for Mathematical Sciences)
Bruno Kahn (Institut de Mathématiques de Jussieu)
Shun-ichi Kimura (Hiroshima University)
Yuken Miyasaka (Tohoku University)
Chikara Nakayama (Tokyo Institute of Technology)
Tomohide Terasoma (The University of Tokyo)
Seidai Yasuda (Research Institute for Mathematical Sciences)
Takuya Yamauchi (Kagoshima University)

Program (* : Joint talk with the department colloquium)

23 (Mon)
13:15-14:15	Shun-ichi Kimura (Hiroshima)	Rationality and irrationality of motivic series
14:30-15:30	Tomoyuki Abe (IPMU)	Langlands program for p-adic coefficients and the petites camarades conjecture
15:30-16:00	(tea)
16:00-17:00 *	Bruno Kahn (IMJ)	On the generalised Hodge and Tate conjectures for products of elliptic curves
24 (Tue)
9:30-10:30	Olivier Brinon (Paris)	Overconvergence of the Hodge-Tate-Igusa map
10:45-11:45	Yuken Miyasaka (Tohoku)	Torsion on Theta Divisors of Hyperelliptic Jacobians and p-adic Tau-Function
11:45-13:15	(lunch)
13:15-14:15	Masanori Asakura (Hokkaido)	Explicit computation of syntomic regulator on K_1 of elliptic surface over a p-adic field
14:30-15:30	Naoki Imai (RIMS)	Representations of conductor three in cohomology of Lubin-Tate spaces of height two
15:30-16:00	(tea)
16:00-17:00	Tomohide Terasoma (Tokyo)	The Universal elliptic curve and convolutions of logarithmic theta functions
25 (Wed)
9:30-10:30	Chikara Nakayama (TIT)	A fiber bundle property of proper log smooth maps (joint work with Arthur Ogus)
10:45-11:45	Takuya Yamauchi (Kagoshima)	L-function of some Siegel threefold of low level: non-neat case
11:45-13:15	(lunch)
13:15-14:15	Seidai Yasuda (RIMS)	Some hypergeometric polynomials and reductions of crystalline representations with moderate Hodge-Tate weights
14:30-15:30	Bruno Kahn (IMJ)	The derived functors of unramified cohomology

Abstracts

Bruno Kahn's first talk: We study the generalised Tate conjecture for products of elliptic curves over a finite field, and the generalised Hodge conjecture for products of elliptic curves over $\mathbf{C}$: the results are parallel. We prove these conjectures if the elliptic curves are ``in good position": this happens in particular if they run among at most 3 isogeny classes. We also prove them for $H^3$, in all cases. Finally, we show how things become more intricate for 4 CM elliptic curves in special position. There appears a new simple 4-dimensional abelian variety, which does not seem to have been considered before.
Olivier Brinon: The classical Hodge-Tate-Igusa (induced by the Hodge-Tate map of the p-divisible group of the universal abelian scheme on the ordinary locus of the Siegel variety of genus g and level N>=3) relates the Igusa tower and the ”coherent” tower. I will explain why it overconverges, after a scalar extension. This is a joint work with F. Mokrane and J. Tilouine.

This workshop is financially supported by:

JSPS Grant-in-aid (B) (22340001)
JSPS Grant-in-Aid for Young Scientists (A) (22684001)
JSPS Grant-in-Aid for Challenging Exploratory Research (21654001)
JSPS Grant-in-Aid for Challenging Exploratory Research (22654001)
Inamori Foundation

Organizers : Nobuo Tsuzuki (Tohoku University), Takao Yamazaki (Tohoku University)