Tokyo-Nagoya Algebra Seminar

Organizer(s) Noriyuki Abe, Aaron Chan, Erik Darpoe, Osamu Iyama, Tsutomu Nakamura, Hiroyuki Nakaoka, Ryo Takahashi

2021/05/06

16:00-17:30   Online
Please see the URL below for details on the online seminar.
Liran Shaul (Charles University)
Derived quotients of Cohen-Macaulay rings (English)
[ Abstract ]
It is well known that if A is a Cohen-Macaulay ring and $a_1,\dots,a_n$ is an $A$-regular sequence, then the quotient ring $A/(a_1,\dots,a_n)$ is also a Cohen-Macaulay ring. In this talk we explain that by deriving the quotient operation, if A is a Cohen-Macaulay ring and $a_1,\dots,a_n$ is any sequence of elements in $A$, the derived quotient of $A$ with respect to $(a_1,\dots,a_n)$ is Cohen-Macaulay. Several applications of this result are given, including a generalization of Hironaka's miracle flatness theorem to derived algebraic geometry.
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html