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:Number Theory Seminar
SUMMARY:Resolution of singularities on the Lubin-Tate towe
r - Jared Weinstein (UCLA)
DTSTART;TZID=Europe/London:20100518T143000
DTEND;TZID=Europe/London:20100518T153000
UID:TALK23458AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/23458
DESCRIPTION:A fundamental result in local class field theory i
s the 1965 paper of Lubin and Tate\, which classif
ies the abelian extensions of a nonarchimedean loc
al field in terms of an algebraic structure known
as a one-dimensional formal module. We'll review
this result\,\nand show how the question of constr
ucting nonabelian extensions leads to the study of
the Lubin-Tate tower\, which can be viewed as an
infinitesimal version of the classical tower of mo
dular curves _X(p^n^)_.\n\nBy results of Harris-Ta
ylor and Boyer\, the cohomology of the Lubin-Tate
tower encodes precise information about non-abelia
n extensions of the local field (namely\, it reali
zes the local Langlands correspondence). The Lubin
-Tate tower has a horribly singular special fiber\
, which hinders any direct study of its cohomology
\, but we will show that after blowing up a singul
arity there is a\nmodel for the tower whose reduct
ion contains a very curious nonsingular hypersurfa
ce defined over a finite field -- curious because
it seems to have the maximum number of rational po
ints relative to its topology. We will write down
the equation for this hypersurface and formulate a
conjecture (alas\, still unproved) regarding its
zeta function.
LOCATION:MR13
CONTACT:Tom Fisher
END:VEVENT
END:VCALENDAR