Event Details

Algebra and Geometry Seminar: Greg Stevenson (Glasgow)

Homological residue fields for tensor triangulated categories

There is an instructive and (miraculously) faithful analogy between commutative rings and tensor triangulated categories. One can speak of prime ideals, the Zariski topology, localization, and the resulting spectra in both contexts and these concepts relate to one another in a way that far exceeds what one would naively, and perhaps reasonably, expect. However, there is trouble in paradise: there is no existing analogue of closed subschemes for tensor triangulated categories and, in particular, residue fields are a problematic concept. I'll give an introduction to this circle of ideas and discuss joint work with Paul Balmer and Henning Krause which is a first step toward producing such residue fields.