Niels Feld | Milnor-Witt sheaves and modules
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 2021-02-11

Seminar on A1-topology, motives and K-theory, February 11, 2021
Niels Feld (Institut Fourier)
Milnor-Witt sheaves and modules

We present a generalization of Rost's theory of cycle modules where we use Milnor-Witt K-theory instead of the classical Milnor K-theory. We obtain a setting to study general cycle complexes and their (co)homology groups. We link this theory with Morel-Voevodsky stable homotopy category and we study homotopy sheaves with generalized transfers. As applications, we discuss a conjecture of Morel about Bass-Tate transfers and a conservativity conjecture due to Bachmann and Yakerson.