Videos

Koszul, Ringel, and Serre duality for strict polynomial functors

Presenter
February 16, 2013
Keywords:
  • commutative algebra
  • noncommutative algebra
  • representation theory
  • homological algebra
  • resolutions of modules
  • duality theorems
  • functor calculus
  • polynomial functor
MSC:
  • 18G35
  • 18G10
  • 18Gxx
  • 16Gxx
  • 18-xx
  • 55U30
Abstract
Strict polynomial functors were introduced by Friedlander and Suslin in their work on the cohomology of finite group schemes. More recently, a Koszul duality for strict polynomial functors has been established by Chalupnik and Touze. In my talk I will give a gentle introduction to strict polynomial functors (via representations of divided powers) and will explain the Koszul duality, making explicit the underlying monoidal structure which seems to be of independent interest. Then I connect this to Ringel duality for Schur algebras and describe Serre duality for strict polynomial functors.