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SUMMARY:Independence-of-ell for attributes of Tannakian monodromy groups o
 f perverse sheaves on commutative algebraic groups [MPIM]
DTSTART:20260930T123000Z
DTEND:20260930T133000Z
DTSTAMP:20260926T014400Z
UID:indico-event-1595@math-events.uni-bonn.de
DESCRIPTION:Speakers: Hyun Jong Kim (University of Western Ontario)\n\nNum
 ber Theory Lunch Seminar\nIn ongoing work with Chris Hall\, we start with 
 a connected\,commutative algebraic group G over a finite field Fq along wi
 th niceperverse sheaves M1 and M2 on G with respectively ell1-adic and ell
 2-adiccoefficients with essentially the same Frobenius eigenvalues at stal
 ks. M1and M2 each generate (arithmetic and geometric) neutral tannakiancat
 egories\, associated to which are tannakian groups G1 and G2\, which areaf
 fine algebraic groups over Qell1bar and Qell2bar. Our goal is to provethat
  attributes\, such as the group of components\, of G1 and G2 are equal toe
 ach other. I will talk about progress that we have made towards suchresult
 s\; in particular\, we expect to show that the groups of connectedcomponen
 ts of the geometric versions of the tannakian groups areisomorphic. Our wo
 rk fundamentally uses Katz's geometric ideas\, originallyused to prove equ
 idistribution theorems of exponential sums of traces ofFrobenius on comple
 xes of ell-adic sheaves on tori over finite fields\, andwork of Forey-Fres
 án-Kowalski\, which generalized Gabber and Loeser'stannakian formalism of
  perverse sheaves from tori to general connectedcommutative algebraic grou
 ps over finite fields to generalize Katz'sequidistribution theorems.\n\nht
 tps://math-events.uni-bonn.de/event/1595/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1595/
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