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SUMMARY:p-adic cohomology over local fields of characteristic p - Chris La
 zda (Imperial College)
DTSTART:20141118T161500Z
DTEND:20141118T171500Z
UID:TALK55159@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:If K is a local field of residue characteristic p\, then every
  l-adic representation (l different from p) of G_K is potentially semistab
 le - this is Grothendieck’s l-adic local monodromy theorem. For p-adic r
 epresentations\, and K of characteristic 0\, potential semistablility is a
  condition that one needs to impose\, and one must then prove that represe
 ntations coming from geometry are potentially semistable. When K is of cha
 racteristic p\, then the natural replacement for p-adic Galois representat
 ions that one encounters when looking at the cohomology of varieties over 
 K are (phi\,nabla) modules over the Amice ring\, and the theory that produ
 ces them is rigid cohomology. We propose a condition on these modules anal
 ogous to potential semistability\, and outline work in progress to show th
 at all (phi\,nabla) modules arising from geometry satisfy this condition. 
 The idea is to replace rigid cohomology by a relative version by looking a
 t compactifications over the ring of integers O_K of K. For varieties over
  K for which one can show finiteness of this theory (currently\, for smoot
 h curves)\, one can then attach Weil-Delinge representations to their coho
 mology\, exactly as in the l-adic and mixed characteristic p-adic cases.\n
LOCATION:MR13
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