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SUMMARY:Wild Hurwitz spaces and level structures [Arithmetic Geometry and 
 Representation Theory Research Seminar]
DTSTART:20260421T130500Z
DTEND:20260421T150500Z
DTSTAMP:20260420T222500Z
UID:indico-event-1220@math-events.uni-bonn.de
DESCRIPTION:Speakers: Michael Temkin\n\nHurwitz moduli spaces of covers of
  curves of degree d are classical and well studied objects \nif one assume
 s that d! is invertible and hence no wild ramification phenomena occur. \n
 There were very few attempts to study the wild case. In the most important
  one Abramovich and Oort \nstarted with the classical space H_{2\,1\,0\,4}
  of double covers of P^1 ramified at four points \nand (following an idea 
 of Kontsevich and Pandariphande) described its schematic closure H \nin th
 e space of stable maps over Z. The result over F_2 was both strange and in
 formative\, but lacked a modular interpretation.\n\nIn the first part of m
 y talk I will describe the example of Abramovich-Oort and the non-archimed
 ean\nperspective on the same example\, and in the second part I will tell 
 about \na work in progress of Hippold\, where a (logarithmic) modular vers
 ion of compactified \nHurwitz space of degree p is constructed when only (
 p-1)! is invertible. In particular\, \nthis conceptually explains phenomen
 a observed by Abramovich-Oort. Then\nI will describe another outcome of th
 e same ideas. It was observed by Abramovich-Oort that H \nis the blowing u
 p of the modular curve X(2). This is not a coincidence\, and the same idea
 s \ncan be used to refine the wild level structures of Drinfeld and constr
 uct modular interpretation \nof the minimal modifications of the curves X(
 p^n) which separate ordinary branches at any supersingular point. \nThis i
 s a very recent work in progress and the precise description of the obtain
 ed spaces is still to be found.\n\nhttps://math-events.uni-bonn.de/event/1
 220/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1220/
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