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SUMMARY:Simon Cooper (King's College London)
DTSTART:20261021T150000Z
DTEND:20261021T160000Z
DTSTAMP:20261018T042430Z
UID:LNTS/204
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/204/">G
 -Zips and Tautological Rings of Shimura Varieties</a>\nby Simon Cooper (Ki
 ng's College London) as part of London number theory seminar\n\nLecture he
 ld in Imperial College London\, Huxley 139.\n\nAbstract\nI will discuss a 
 conjecture describing the tautological ring of a Shimura variety and prese
 nt recent progress towards the conjecture. This is the subject of joint wo
 rk with W. Goldring. The tautological ring is the subring of the Chow ring
  generated by all Chern classes of all automorphic vector bundles. It has 
 been completely described for the Siegel modular variety by work of van de
 r Geer. An important feature is that more is known in positive characteris
 tic than in characteristic zero. This is because the mod p special fibre o
 f the Shimura variety admits a "zip period map" into the stack of G-Zips\,
  which is a mod p analogue of the classical period map in Hodge theory. I 
 will explain how the theory of G-Zips can be used to deduce significant in
 formation about the tautological ring.\n
LOCATION:https://researchseminars.org/talk/LNTS/204/
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