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SUMMARY:Eric Katz (Ohio State)
DTSTART;VALUE=DATE-TIME:20210521T190000Z
DTEND;VALUE=DATE-TIME:20210521T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123135Z
UID:agstanford/50
DESCRIPTION:Title: Iterated p-adic integration on semistable curves\nby Eric Katz (Oh
io State) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nHo
w do you integrate a 1-form on an algebraic curve over the p-adic numbers?
One can integrate locally\, but because the topology is totally disconnec
ted\, it's not possible to perform analytic continuation. For good reducti
on curves\, this question was answered by Coleman who introduced analytic
continuation by Frobenius. For bad reduction curves\, there are two notion
s of integration: a local theory that is easy to compute\; and a global si
ngle-valued theory that is useful for number theoretic applications. We di
scuss the relationship between these integration theories\, concentrating
on the p-adic analogue of Chen's iterated integration which is important f
or the non-Abelian Chabauty method. We explain how to use combinatorial id
eas\, informed by tropical geometry and Hodge theory\, to compare the two
integration theories and outline an explicit approach to computing these i
ntegrals. This talk will start from the beginning of the story and require
s no background besides some fluency in algebraic geometry and topology. T
his is joint work with Daniel Litt.\n\nThe synchronous discussion for Eric
Katzâ€™s talk is taking place not in zoom-chat\, but at https://tinyurl.c
om/2021-05-21-ek (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/50/
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