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DTSTAMP:20260424T143212Z
UID:648ae4751a1f6301683688@ist.ac.at
DTSTART:20241205T130000
DTEND:20241205T150000
DESCRIPTION:Speaker: Seguin Béranger\nhosted by Tim Browning\nAbstract: Th
 e asymptotic distribution of field extensions (often counted by discrimina
 nt) is a well-studied topic that aims to make the predictions of inverse G
 alois theory quantitative. Over number fields\, precise conjectures (and p
 artial results) give a clear idea of the situation (Wright\, Malle\, Bharg
 ava\, ...). A similar picture emerges for tamely ramified extensions of fu
 nction fields (Ellenberg\, Tran\, Venkatesh\, and Westerland).In contrast\
 , the wildly ramified case remains a terra incognita: the case of abelian 
 extensions was only recently solved (Lagemann\, Klners-Mller\, Potthast\, 
 Gundlach) using class field theory.In this talk\, we fix a prime p>2\, and
  we focus on p-groups G of nilpotency class 2 (the "most abelian" among no
 n-abelian p-groups). We explain how to parametrize G-extensions of fields 
 of characteristic p using Lie algebras and Witt vectors.Work by Abrashkin 
 describes the ramification filtration of these extensions and reduces the 
 counting problem (over local fields) to a "typical" arithmetic geometry pr
 oblem: counting solutions to polynomial equations over finite fields.We pr
 esent several instances where this local counting can be carried out.If ti
 me permits\, we will also discuss results over global function fields\, wh
 ich follow from the local case via a local-global principle.This work is a
  joint collaboration with Fabian Gundlach.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Seguin Béranger: Asymptotic distribution of wildly ramified extens
 ions of function fields.
URL:https://talks-calendar.ista.ac.at/events/5421
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