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


15:15:00 - 16:15:00

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.