Anand Sawant
University of Munich, Germany
September 14, 2017
Central extensions and $\mathbb A^1$-fundamental groups: Classical results of Matsumoto and Suslin describe the universal central extension of the group of rational points of a split, semisimple, simply connected algebraic group. These results were later extended by Brylinski and Deligne, who determined the category of central extensions of a reductive group by the second $K$-theory sheaf $K_2$. We will discuss how these classical results can be uniformly explained and generalized using the so-called motivic or $\mathbb A^1$-fundamental group of a reductive algebraic group and describe some interesting consequences. The talk is based on joint work in progress with Fabien Morel.
University of Munich, Germany
September 14, 2017
Central extensions and $\mathbb A^1$-fundamental groups: Classical results of Matsumoto and Suslin describe the universal central extension of the group of rational points of a split, semisimple, simply connected algebraic group. These results were later extended by Brylinski and Deligne, who determined the category of central extensions of a reductive group by the second $K$-theory sheaf $K_2$. We will discuss how these classical results can be uniformly explained and generalized using the so-called motivic or $\mathbb A^1$-fundamental group of a reductive algebraic group and describe some interesting consequences. The talk is based on joint work in progress with Fabien Morel.