|Date: Wednesday, January 04, 2017
Location: 4096 East Hall (4:10 PM to 5:30 PM)
Title: Polynomial functors and algebraic K-theory
Abstract: The Grothendieck group K_0 of a commutative ring is well-known to be a \lambda-ring: although the exterior powers are non-additive, they induce maps on K_0 satisfying various universal identities. The \lambda-operations are known to give homomorphisms on higher K-groups.
In joint work in progress with Barwick, Glasman, and Nikolaus, we give a general framework for such operations. Namely, we show that the K-theory space is naturally functorial for polynomial functors, and describe a universal property of the extended K-theory functor. This extends an earlier algebraic result of Dold for K_0. In this picture, the \lambda-operations are precisely those given by the "strict polynomial functors" of Friedlander-Suslin.
Speaker: Akhil Mathew
Institution: Harvard University