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SUMMARY:Ana Caraiani (Imperial College London)
DTSTART:20211005T100000Z
DTEND:20211005T110000Z
DTSTAMP:20260423T021218Z
UID:ZAG/152
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/152/">On
  the cohomology of Hilbert modular varieties with torsion coefficients</a>
 \nby Ana Caraiani (Imperial College London) as part of ZAG (Zoom Algebraic
  Geometry) seminar\n\n\nAbstract\nShimura varieties are certain moduli spa
 ces equipped with many symmetries\, that play an important role in the Lan
 glands programme. For example\, Hilbert modular varieties are quotients of
  the product of several copies of the upper-half plane by certain arithmet
 ic groups. I will discuss a general conjecture on the cohomology of Shimur
 a varieties with torsion coefficients\, which states that the non-degenera
 te part of their cohomology is concentrated in the middle degree. I will g
 ive an overview of an approach to this conjecture introduced in joint work
  with Peter Scholze. This approach relies on the geometry of the Hodge-Tat
 e period morphism\, which I will describe\, and on certain technical compu
 tations. I will then specialise to the case of Hilbert modular varieties a
 nd explain a modified version of this approach that relies on an instance 
 of geometric Jacquet-Langlands functoriality for the fibers of the Hodge-T
 ate period morphism. This is joint work with Matteo Tamiozzo.\n
LOCATION:https://researchseminars.org/talk/ZAG/152/
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