Vector bundles on punctured spectrum of local rings

Thời gian: 17h15-18h30, thứ năm, 06/07/2023

Hình thức: Offline tại phòng 612 A6 và online qua google meet, cụ thể https://meet.google.com/yep-kbzk-eao?pli=1&authuser=1

Tóm tắt: Let $(R,m)$ be a local Noetherian rings. In this talk, I will discuss the category of reflexive modules that are locally free of constant rank on the punctured spectrum of $R$. Even in dimension one, this category is poorly understood until quite recently (and will be discussed in my talk at the Algebra seminar on Wednesday). When the depth of $R$ is at most $2$, such category is equivalent to the category of vector bundles on the punctured spectrum of $R$. This point of view has connected many simple statements in commutative algebra to modern topics: Picard groups, Brauer groups, Nori fundamental group schemes, etc. I will sketch these and other connections to algebraic geometry and singularity theory.