Colloquium

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Organizer(s) ABE Noriyuki, IWAKI Kohei, KAWAZUMI Nariya (chair), KOIKE Yuta
URL https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index_e.html

2023/03/13

13:00-17:00   Hybrid
Registration for online participation: [Reference URL], Application for onsite participation: https://forms.gle/2eDKDtNsTounyoXw6 (Update: Mar. 5)
Masahiko Kanai ( Graduate School of Mathematical Sciences, the University of Tokyo) 13:00-14:00
(JAPANESE)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZElcO2oqTgoG9a1JSawX0kFRMSFheEptcaA
Hisashi Inaba (Graduate School of Mathematical Sciences, the University of Tokyo) 14:30-15:30
(JAPANESE)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIkceigrj4tEt0AydbnE8PVJmIS6xLanDAe
Shuji Saito ( Graduate School of Mathematical Sciences, the University of Tokyo) 16:00-17:00
From higher dimensional class field theory to a new theory of motives (ENGLISH)
[ Abstract ]
My first research was on Higher Dimensional Class Theory done in collaboration with Kazuya Kato. That was 40 years ago. The classical class field theory is a theory that controls the Galois group of the maximal abelian extension of a number field (a finite extension of the field of rational numbers) using only information intrinsic to the field (e.g., its ideal class group). Higher dimensional class field theory is an extension of this theory to the case of finitely generated fields over the field of rational numbers or a finite field. It is formulated as an arithmetic algebro-geometric problem using scheme theory.

In this talk, I will start with a review of the classical class field theory that can be understood by undergraduates and explain how higher dimensional class field theory is formulated in a way that is easy to understand even for non-specialists. I will also briefly explain an improvement of Kato-Saito's higher-dimensional class field theory that I made with Moritz Kerz in 2016, and how it triggered a recent new development of theory of motive. In particular, I will discuss the relationship between the new theory and ramification theory (of which Takeshi Saito is a world leader), which until now has had no interaction with theory of motives.
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZAqf-ioqz8jG9BWefiIf_zTJ1t7R7VG1beV