Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups

An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fields

Exponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a century to Kloosterman. Grothendieck’s creation of the machinery of l-adic cohomology led to the understanding that families of exponential sums give rise to local systems, while Deligne, who gave his general equidistribution theorem after proving...