Algebra Seminar

Friday, November 3, 2017
1:20 PM - 4:00 PM (ET)
Exley Science Center Tower ESC 618
Event Type
Canalia, Caryn

Jonathan Huang, Wes

A Macdonald formula for zeta functions of varieties over finite fields

Abstract:  We provide a formula for the generating series of the zeta function Z(X, t) of symmetric powers Symn X of varieties over finite fields. This realizes Z(X, t) as an exponentiable motivic measure whose associated Kapranov motivic zeta function takes values in W(R) the big Witt ring of R = W(). We apply our formula to compute Z (Symn X, t) in a number of explicit cases. Moreover, we show that all λ-ring motivic measures have zeta functions which are exponentiable. In this setting, the formula for Z(X, t) takes the form of a MacDonald formula for the zeta function. 

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