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CATEGORIES:Conferences/Seminars/Lectures
DESCRIPTION:Amnon Besser (Ben-Gurion University/Georgia Tech)\n\nTitle: "Vo
logodsky and Coleman integration on curves with semi-stable reduction"\n\nA
bstract: A meromorphic one-form on a curve over a p-adic field with semi-st
able reduction has two p-adic integrals associated to it\, by Coleman and b
y Vologodsky. We prove that the Vologodsky integral restricts to Coleman in
tegrals on the rigid subdomains reducing to the components of the smooth pa
rt of the special fiber and that on the connecting annuli the differences o
f these Coleman integrals form a harmonic cochain on the edges of the dual
graph of the special fiber. This determines the Vologodsky integral complet
ely. I will explain the behavior of the Vologodsky integral on the connecti
ng annuli which has been observed independently and used\, by Stoll\, Katz-
Rabinoff-Zureick-Brown\, in works on global bounds on the number of rationa
l points on curves. I will describe an interesting product on 1-forms used
in the proof of the Theorem as well as in work on p-adic height pairings.
I will explain the original motivation for this result\, which is relevant
for the interesting question of generalizing the result to iterated integra
ls (Joint work with Sarah Zerbes).
DTEND:20171128T223000Z
DTSTAMP:20180816T123249Z
DTSTART:20171128T213000Z
LOCATION:2-143
SEQUENCE:0
SUMMARY:MIT Number Theory Seminar
UID:tag:localist.com\,2008:EventInstance_3186820
URL:http://calendar.mit.edu/event/mit_number_theory_seminar_6586
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