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SUMMARY:Oli Gregory (Imperial College London)
DTSTART:20230426T150000Z
DTEND:20230426T160000Z
DTSTAMP:20260418T063754Z
UID:LNTS/96
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/96/">A 
 semistable variational p-adic Hodge conjecture</a>\nby Oli Gregory (Imperi
 al College London) as part of London number theory seminar\n\nLecture held
  in KCL\, Strand Building\, Room S3.30.\n\nAbstract\nLet $k$ be a perfect 
 field of characteristic $p>0$\, and let $X$ be a proper scheme over $W(k)$
  with semistable reduction. I shall formulate an analogue of the Fontaine-
 Messing variational p-adic Hodge conjecture in this setting. To get there\
 , I shall define a logarithmic version of motivic cohomology for the speci
 al fibre $X_k$. This theory is related to relative log-Milnor K-theory\, l
 ogarithmic Hyodo-Kato Hodge-Witt cohomology\, and log K-theory. With this 
 in hand\, I shall prove the deformational part of the conjecture\, simulta
 neously generalising the semistable $p$-adic Lefschetz $(1\,1)$ theorem of
  Yamashita (the case $r=1$) and the deformational $p$-adic Hodge conjectur
 e of Bloch-Esnault-Kerz (the good reduction case). This is joint work with
  Andreas Langer.\n
LOCATION:https://researchseminars.org/talk/LNTS/96/
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