Equidistribution of exponential sums on commutative algebraic groups (after Katz)


Claude Sabbah  ( École Polytechnique, France )
2017-11-01  15:15 - 16:15
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

Many exponential sums, such as Gauss sums or Kloosterman sums, appear as the Fourier transform of the trace function of an l-adic sheaf on a commutative algebraic group over a finite field. I will discuss equidistribution results for these sums when the l-adic sheaf is fixed but the character with respect to which the Fourier transform is taken varies. Most of the talk will be devoted to present a series of recent works by Katz where Tannakian ideas play a pivotal role. If time permits, I will also explain some new results.