**Abstract:** A^1- (or motivic) homotopy theory is a homotopy theory for schemes developed by Morel and Voevodsky in 1990's in which the affine line plays the role of the unit interval. In this lecture, we will study the sheaf of A^1-connected components of a scheme. There are various notions of connectedness in this theory and it is natural to ask whether these objects have nice properties such as homotopy invariance and whether they are birational invariants of smooth proper schemes. We will discuss conjectures of Morel and Asok-Morel regarding A^1-connected components of a scheme. This is a report on a joint work with Chetan Balwe and Amit Hogadi.

Feb 10, 2014 | 04:15 PM

SR 119, Arnimallee 3