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SUMMARY:Evan O'Dorney (Princeton University)
DTSTART:20210527T210000Z
DTEND:20210527T220000Z
DTSTAMP:20260423T041113Z
UID:UCSD_NTS/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/39/
 ">Arithmetic statistics of $H^1(K\, T)$</a>\nby Evan O'Dorney (Princeton U
 niversity) as part of UCSD number theory seminar\n\nLecture held in normal
 ly APM 7321\, currently online.\n\nAbstract\nCoclasses in a Galois cohomol
 ogy group $H^1(K\, T)$ parametrize extensions of a number field with certa
 in Galois group. It is natural to want to count these coclasses with gener
 al local conditions and with respect to a discriminant-like invariant. In 
 joint work with Brandon Alberts\, I present a novel tool for studying this
 : harmonic analysis on adelic cohomology\, modeled after the celebrated us
 e of harmonic analysis on the adeles in Tate's thesis. This leads to a mor
 e illuminating explanation of a fact previously noticed by Alberts\, namel
 y that the Dirichlet series counting such coclasses is a finite sum of Eul
 er products\; and we nail down the asymptotic count of coclasses in satisf
 ying generality.\n\nIn the pre-talk\, I will give a rundown on the needed 
 background in Galois cohomology\, etale algebras\, the local Tate pairing\
 , and Poitou-Tate duality.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/39/
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