Ambrus Pal's series lecture

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Speaker: Ambrus Pal (Imperial College)
Date:19(Tue)-22(Fri)/June/2007, 15:00-16:30
Place: Research Institute for Mathematical Sciences, Kyoto University, Kyoto
Room 202 on Tuesday, Room 009 on Wednesday and Thursday, Room 115 on Friday

Title:
"Special values of p-adic L-functions in positive characteristic"

Abstract:
In spite of their importance, there has not been a real breakthrough on the conjectures of Artin-Tate, Parshin, Tate and Beilinson on algebraic cycles and related K-groups in positive characteristic since they were formulated. In my talks I will try to describe a program whose eventual goal is to make progress on these conjectures via formulating a refined set of conjectures which give hints where we should look for those algebraic cycles which are predicted by the original conjectures, and hence enable us to find them.

This series lecture is supported by JSPS (B)#17340008 "数論的多様体の$p$進的手法による研究" (representative Nobuo Tsuzuki).

We will take dinner with Pal on Tuesday.

He will also give a talk titled as
"A p-adic Langlands correspondence in characteristic p"
on the Workshop on Motives 3-rd (2-6/July/2007)
at University of Tokyo.

Titles and Abstracts of Talks:

19(Tue)/June 15:00--16:30 at room 202:
"Non-archimedean L-functions and periods"

Abstract: I will describe an analogue of the p-adic L-function of elliptic curves and show how one may use modular parametrizations by Drinfeld modular curves to prove an analogue of the exceptional zero conjecture.


20(Wed)/June 15:00--16:30 at room 009:
"Rigid-analytic regulators"

Abstract: The aim of this second talk is to demonstrate that there is a rich theory of rigid analytic regulators which are much more closely analogous to usual theory of regulators in characteristic zero than the cohomological constructions used in the above-mentioned set of conjectures.


21(Thu)/June 15:00--16:30 at room 009:
"An analogue of Beilinson's theorem on K2 of elliptic curves"

Abstract: I'll will talk about a refined non-archimedean analogue of the result in the title for elliptic curves over function fields of one variable which involves the regulator introduced in the previous talk. Hopefully the audience will see that we are on the right track since once the basic definitions are made it is very straightforward to find the analogue of every step in the classical situation.


22(Fri)/June 15:00--16:30 at room 115:
"Refined conjectures of the type of Beilinson and Swinnerton-Dyer-Birch"

Abstract: Depending on how much time is left after I'm finished with the previous subject, I will talk about some general conjectures for elliptic curves which are in some sense better analogues of the classical conjectures in positive characteristic and discuss what can be done about them.

Host: G. Yamashita(RIMS),