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SUMMARY:Green Forms for Special Cycles on Shimura Varieties
DTSTART;VALUE=DATE-TIME:20180509T123000Z
DTEND;VALUE=DATE-TIME:20180509T133000Z
DTSTAMP;VALUE=DATE-TIME:20210413T172559Z
UID:indico-event-3504@indico.math.cnrs.fr
DESCRIPTION:The arithmetic geometry of Shimura varieties has been intensiv
ely studied since\, about twenty years ago\, Kudla made some conjectures r
elating their arithmetic Chow groups with derivatives of Eisenstein series
and of Rankin-Selberg L-functions. The conjectures concern special cycles
in orthogonal and unitary Shimura varieties and predict in particular tha
t Green currents for these cycles should exist satisfying some additional
properties\, including an explicit expression for archimedean height pairi
ngs.\n\nI will explain how to attach a natural superconnection to each spe
cial cycle and how results of Quillen and further developments by Bismut\,
Gillet and Soule allow to define natural Green forms for special cycles.
For compact Shimura varieties with underlying group O(p\,2) or U(p\,1) I w
ill explain how to compute the resulting archimedean heights and relate th
em to derivatives of Eisenstein series\, essentially settling the archimed
ean aspect of Kudla's conjectures in this case. This is joint work with Si
ddarth Sankaran.\n\nhttps://indico.math.cnrs.fr/event/3504/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/3504/
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