On the completely reducible subgroups and applications

Thời gian: 10:00 đến 11:00 Ngày 31/07/2018

Địa điểm: B4-705, VIASM

Báo cáo viên: Dao Phuong Bac

Tóm tắt:

Let k be an arbitrary field, H a k-subgroup of a given connected reductive group G. We say that H is G-completely reducible over k (proposed by J.-P. Serre (1997)) if whenever H is contained in a k-parabolic subgroup P of G, there exists a k-Levi subgroup L of P containing H. When k is algebraically closed and G = GL(V ), H is G-completely reducible if and only if V is H-completely reducible in the usual sense. In this talk, we present some recent results due to M. Bate, S. Herpel, B. Martin, G. Rohrle, R. Tange, T. Uchiyama, regarding behavior of completely reducible notion via base change, and its applications in studying the connections of closedness between geometric and relative orbits in the case of local base fields.