Moduli spaces of semistable sheaves with fixed rank and determinant: their existence and rational points

Inder Kaur
IMPA 
Abstract:
It is well-known that the moduli space of semistable sheaves of fixed rank and degree on a variety may be empty. In this talk I will discuss the existence of semistable vector bundles of fixed rank and determinant on a fibered surface defined over a Henselian discrete valuation ring, under certain assumptions. I will also outline the difficulties in defining a moduli space with fixed determinant on a singular variety and a possible solution to the problem.