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SUMMARY:Pol van Hofton (King's College London)
DTSTART:20210329T170000Z
DTEND:20210329T175000Z
DTSTAMP:20260423T041508Z
UID:UCLA_NTS/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/26/
 ">Monodromy and irreducibility of Igusa varieties</a>\nby Pol van Hofton (
 King's College London) as part of UCLA Number Theory Seminar\n\n\nAbstract
 \nIgusa varieties are smooth varieties in characteristic $p$ arising natur
 ally as covers of certain subvarieties (central leaves) of Shimura varieti
 es\, for example of the ordinary locus of the modular curve. The $\\ell$-a
 dic cohomology of Igusa varieties acts as a bridge between the cohomology 
 of Rapoport-Zink spaces (local) and the cohomology of Shimura varieties (g
 lobal)\, and it is therefore very interesting to study this cohomology. In
  this talk I will discuss recent joint work with Luciena Xiao Xiao\, where
  we compute the 0th cohomology group. This is equivalent to determining th
 e irreducible components of Igusa varieties\, and our results generalise r
 esults of Hida and Chai-Oort. Our strategy combines recent work of D’Add
 ezio on monodromy of compatible local systems with a generalisation of a m
 ethod of Hida\, and the Honda-Tate theory for Shimura varieties of Hodge t
 ype of Kisin--Madapusi Pera--Shin.\n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/26/
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