Stephen McKean | Lifts, transfers, and degrees in motivic homotopy
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 2022-04-15

Seminar on A1-topology, motives and K-theory, April 15, 2022
Stephen McKean (Duke University)
Lifts, transfers, and degrees in motivic homotopy

Morel’s A1-degree, which is a generalization of the Brouwer degree, is a fundamental tool in the application of motivic homotopy theory to enumerative geometry. A natural question to ask is how the A1-degree behaves under field extensions and transfers. This question is completely answered for separable field extensions (due to joint work with Brazelton, Burklund, Montoro, and Opie) and for simple extensions in dimension 1 (recent joint work with Brazelton). We will discuss what is known about this problem, as well as remaining open questions.