Algebraic K-Theory Seminar
Elden Elmanto
Harvard
The cdarc topology
Abstract: The excision problem asks for when a functor defined on schemes converts (pro-)Milnor squares to (pro-)pullback squares. This has computational ramifications; the solution for algebraic K-theory yields a proof of Weibel's conjecture. We give a mechanism for checking Milnor excision using a topology called cdarc topology. This bears an analogous relationship to Bhatt and Mathew's arc topology as the one enjoyed between the Nisnevich topology and the etale topology. We will discuss a theorem which makes precise the idea that "cdh + henselian-v-excision = Milnor excision." An application includes cases of Milnor excision for motivic spectra. This is joint work with Marc Hoyois, Shane Kelly and Ryomei Iwasa.
Wednesday November 20, 2019 at 3:00 PM in 1227 SEO