BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Toroidal compactifications and incompressibility o
f exceptional congruence covers. - Patrick Brosnan
(University of Maryland\, College Park\; Universi
ty of Maryland\, College Park)
DTSTART;TZID=Europe/London:20200120T150000
DTEND;TZID=Europe/London:20200120T160000
UID:TALK137779AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/137779
DESCRIPTION:Suppose a finite group G acts faithfully on an irr
educible variety X. We say that the G-variety X is
compressible if there is a dominant rational morp
hism from X to a faithful G-variety Y of strictly
smaller dimension. Otherwise we say that X is inco
mpressible. In a recent preprint\, Farb\, Kisin a
nd Wolfson (FKW) have proved the incompressibility
of a large class of covers related to the moduli
space of principally polarized abelian varieties w
ith level structure. Their arithmetic methods\, wh
ich use Serre-Tate coordinates in an ingenious way
\, apply to diverse examples such as moduli spaces
of curves and many Shimura varieties of Hodge typ
e. My talk will be about joint work with Fakhruddi
n and Reichstein\, where our goal is to recover so
me of the results of FKW via the fixed point metho
d from the theory of essential dimension. More spe
cifically\, we prove incompressibility for some Sh
imura varieties by proving the existence of fixed
points of finite abelian subgroups of G in smooth
compactifications. Our results are weaker than th
e results of FKW for Hodge type Shimura varieties\
, because the methods of FKW apply in cases where
there is no boundary\, while we need a nonempty bo
undary to find fixed points. However\, our method
has the advantage of extending to many Shimura va
rieties which are not of Hodge type\, in particula
r\, those associated to groups of type E7. Moreove
r\, by using Pink'\;s extension of the Ash\, Mu
mford\, Rapoport and Tai theory of toroidal compac
tifications to mixed Shimura varieties\, we are ab
le to prove incompressibility for congruence cover
s corresponding to certain universal families: e.g
.\, the universal families of principally polarize
d abelian varieties.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
END:VEVENT
END:VCALENDAR