Finitely Presented Groups in Arithmetic Geometry
Mark Shusterman - Harvard University
We discuss the problem of determining the number of generators and relations of several profinite groups of arithmetic and geometric origin. These include etale fundamental groups of smooth projective varieties, absolute Galois groups of local fields, and Galois groups of maximal unramified extensions of number fields. The results are based on a cohomological presentability criterion of Lubotzky, and draw inspiration from well-known facts about three-dimensional manifolds, as in arithmetic topology.
The talk is based on a joint work with Esnault and Srinivas, on a joint work with Jarden, and on work of Yuan Liu.