Chetan Balwe | Geometric criteria for A^1-connectedness
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 04/03/2021

Seminar on A1-topology, motives and K-theory, March 4, 2021
Chetan Balwe (IISER Mohali)
Geometric criteria for A^1-connectedness

We prove that for a large class of varieties, A^1-connectedness can be characterized as the condition that the generic point of the variety can be connected to a k-rational point by an A^1-homotopy. As an application, we will show that over an algebraically closed field of characteristic zero, given any smooth, proper A^1-connected variety, the smooth models of its symmetric powers are also A^1-connected. This can be applied to deduce that the norm varieties constructed by Rost are A^1-connected (over an algebraically closed field of characteristic zero). This talk is based on joint work with Amit Hogadi and Anand Sawant.