第1回

日時

2024年5月29日(水) 15:30~17:00

場所

i-Siteなんば S1 (およびZoomのハイブリッド形式の予定)

講演者

朝永 龍 氏 (東京大学)

タイトル

Cohen-Macaulay representations of quotient singularities admitting field extensions

アブストラクト

The two-dimensional quotient singularities provide examples of rings of finite Cohen-Macaulay type. Furthermore, the Auslander-Reiten quivers of the categories of Cohen-Macaulay modules coincide with the McKay quivers (algebraic McKay correspondence). Conversely, two-dimensional Cohen-Macaulay local rings of finite Cohen-Macaulay type are precisely quotient singularities if their residue fields are algebraically closed and of characteristic zero. In this talk, we generalize the above classical results to situations where the coefficient fields are not necessarily algebraically closed by introducing quotient singularities admitting field extensions. Moreover, we will see how to draw the McKay quivers in this new setting through determining irreducible representations of skew group algebras.

2024年度