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CATEGORIES:Number Theory Seminar
SUMMARY:The formalism of Shimura varieties - Richard Taylo
r\, Stanford University
DTSTART;TZID=Europe/London:20220503T143000
DTEND;TZID=Europe/London:20220503T153000
UID:TALK172220AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/172220
DESCRIPTION:This is joint work with Jack Sempliner. In the 197
0's Deligne proposed a formalism for Shimura varie
ties and Langlands conjectured a formula for the a
ction of Galois on them. Deligne's formalism invol
ves `Shimura data' which parametrizes a Shimura to
gether with a preferred embedding of its field of
definition into the complex numbers. We propose a
different formalism that directly parametrizes a S
himura variety over any field of characteristic 0.
To this end we have to revisit the theory of conj
ugation of Shimura varieties conjectured by Langla
nds and established by Milne and others. We hope t
hat our reformulation of this work also helps to c
larify the theory. A key tool is Kottwitz's defini
tion of the groups B(G).\n\nIn this talk I will sk
etch the formalism of Deligne and Langlands and po
int out what we see as its shortcomings. I will th
en introduce Kottwitz's cohomology theory for exte
nsions of Galois groups\, and explain how to make
cocycles a canonical object\, not just cohomology
classes. Finally I shall explain a reformulation o
f the theory of conjugation of Deligne's Shimura v
arieties and propose an alternative formalism for
Shimura varieties.
LOCATION:MR13
CONTACT:Rong Zhou
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