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CATEGORIES:Number Theory Seminar
SUMMARY:p-adic cohomology over local fields of characteris
tic p - Chris Lazda (Imperial College)
DTSTART;TZID=Europe/London:20141118T161500
DTEND;TZID=Europe/London:20141118T171500
UID:TALK55159AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/55159
DESCRIPTION:If K is a local field of residue characteristic p\
, then every l-adic representation (l different fr
om p) of G_K is potentially semistable - this is G
rothendieck’s l-adic local monodromy theorem. For
p-adic representations\, and K of characteristic 0
\, potential semistablility is a condition that on
e needs to impose\, and one must then prove that r
epresentations coming from geometry are potentiall
y semistable. When K is of characteristic p\, then
the natural replacement for p-adic Galois represe
ntations that one encounters when looking at the c
ohomology of varieties over K are (phi\,nabla) mod
ules over the Amice ring\, and the theory that pro
duces them is rigid cohomology. We propose a condi
tion on these modules analogous to potential semis
tability\, and outline work in progress to show th
at all (phi\,nabla) modules arising from geometry
satisfy this condition. The idea is to replace rig
id cohomology by a relative version by looking at
compactifications over the ring of integers O_K of
K. For varieties over K for which one can show fi
niteness of this theory (currently\, for smooth cu
rves)\, one can then attach Weil-Delinge represent
ations to their cohomology\, exactly as in the l-a
dic and mixed characteristic p-adic cases.\n
LOCATION:MR13
CONTACT:Jack Thorne
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