Noncommutative Geometry Seminar

Date: April 22, 2015

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Amnon Neeman, Australian National University

  

Title: Separable monoids come from etale covers

Abstract:

Given a monoidal category (a category with a tensor product), it is possible to define what it means for an object to be an "separable monoid". We will recall the definition. In the category of modules over a commutative ring the concept is classical and has been studied extensively, with literature going back to the 1960s.

Recently Balmer and some collaborators started the study of separable monoids in any tensor triangulated category; we will recall some of the recent theorems. The main new result I will present says [among other things] that, in the derived category of modules over a noetherian commutative ring, any COMMUTATIVE separable monoid must come from an etale extension of the ring. We will explain this precisely.

Of course there are plenty of noncommutative separable monoids, and the question I would like to draw attention to, in this talk, is what should be the correct general statement.