BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Toroidal compactifications and incompressibility of exceptional co
 ngruence covers. - Patrick Brosnan (University of Maryland\, College Park\
 ; University of Maryland\, College Park)
DTSTART:20200120T150000Z
DTEND:20200120T160000Z
UID:TALK137779@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Suppose a finite group G acts faithfully on an irreducible var
 iety X. We say that the G-variety X is compressible if there is a dominant
  rational morphism from X to a faithful G-variety Y of strictly smaller di
 mension. Otherwise we say that X is incompressible.  In a recent preprint\
 , Farb\, Kisin and Wolfson (FKW) have proved the incompressibility of a la
 rge class of covers related to the moduli space of principally polarized a
 belian varieties with level structure. Their arithmetic methods\, which us
 e Serre-Tate coordinates in an ingenious way\, apply to diverse examples s
 uch as moduli spaces of curves and many Shimura varieties of Hodge type. M
 y talk will be about joint work with Fakhruddin and Reichstein\, where our
  goal is to recover some of the results of FKW via the fixed point method 
 from the theory of essential dimension. More specifically\, we prove incom
 pressibility for some Shimura varieties by proving the existence of fixed 
 points of finite abelian subgroups of G in smooth compactifications.  Our 
 results are weaker than the results of FKW for Hodge type Shimura varietie
 s\, because the methods of FKW apply in cases where there is no boundary\,
  while we need a nonempty boundary to find  fixed points. However\, our me
 thod has the advantage of extending to many Shimura varieties which are no
 t of Hodge type\, in particular\, those associated to groups of type E7. M
 oreover\, by using Pink&#39\;s extension of the Ash\, Mumford\, Rapoport a
 nd Tai theory of toroidal compactifications to mixed Shimura varieties\, w
 e are able to prove incompressibility for congruence covers corresponding 
 to certain universal families: e.g.\, the universal families of principall
 y polarized abelian varieties. 
LOCATION:Seminar Room 2\, Newton Institute
END:VEVENT
END:VCALENDAR