## Ambrus Pal 氏(Imperial College)連続講義のご案内

Title

**
Special values of p-adic L-functions in positive characteristic
**

Date

６月１９日（火）〜２２日（金）１５：００〜１６：３０

Room

京都大学数理解析研究所 ２０２号室（火）, ００９号室（水・木）, １１５号室（金） （曜日によって部屋が異なるのでご注意下さい。）

Speaker

Ambrus Pal (Imperial College)

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.

Comments

○火曜日にPal氏を囲んでの夕食を企画しております。○また、本連続講義の翌々週、 Pal氏は東京大学数理科学研究科である「モチーフの勉強会第３回」 において 「A p-adic Langlands correspondence in characteristic p」 という題目で講演することも付言致します。

○各曜日の題目と要旨：

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.

京都大学数理解析研究所