A semistable variational p-adic Hodge conjecture

Abstract: Let $k$ 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 special fibre $X_k$. This theory is related to relative log-Milnor K-theory, logarithmic Hyodo-Kato Hodge-Witt cohomology, and log K-theory. With this in hand, I shall prove the deformational part of the conjecture, simultaneously generalising the semistable $p$-adic Lefschetz $(1,1)$ theorem of Yamashita (the case $r=1$) and the deformational $p$-adic Hodge conjecture of Bloch-Esnault-Kerz (the good reduction case). This is joint work with Andreas Langer.

number theory

Audience: researchers in the topic

London number theory seminar

Series comments: For reminders, join the (very low traffic) mailing list at mailman.ic.ac.uk/mailman/listinfo/london-number-theory-seminar

For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html