北大数論セミナー：On Tamagawa numbers of tori attached to CM algebras(沖 泰裕氏)

time：16:00-17:00

Place：理学部3号館3-210

Speaker：沖 泰裕 氏（北海道大学）

Title：On Tamagawa numbers of tori attached to CM algebras

Abstract：
The notion of Tamagawa numbers is one of the most important subject in arithmetic of tori over number fields. In 1963, Takashi Ono predicted that all positive rational numbers are realized as the Tamagawa numbers of tori over number fields. This conjecture was resolved by Shin-ichi Katayama in 1985. In this talk, we introduce “tori attached to CM algebras”, which are defined over the field of rational numbers, and give an analogue of Ono’s conjecture/Katayama’s theorem for such tori. More precisely, we explain that every power of 2 can be written as the Tamagawa number of a torus attached to a CM algebra. This talk is based on the joint work with Pei-Xin Liang, Hsin-Yi Yang and Chia-Fu Yu.

Organizer：跡部 発、安田 正大