BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Alexander Petrov (Massachusetts Institute of Technology)
DTSTART:20241112T213000Z
DTEND:20241112T223000Z
DTSTAMP:20260423T130646Z
UID:MITNT/102
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/102/">
 Characteristic classes of p-adic local systems</a>\nby Alexander Petrov (M
 assachusetts Institute of Technology) as part of MIT number theory seminar
 \n\nLecture held in Room 2-449 in the Simons Building (building 2).\n\nAbs
 tract\nGiven an étale $\\mathbb{Z}_p$-local system of rank $n$ on an alge
 braic variety $X$\, continuous cohomology classes of the group $GL_n(\\mat
 hbb{Z}_p)$ give rise to classes in (absolute) étale cohomology of the var
 iety. These characteristic classes can be thought of as p-adic analogs of 
 Chern-Simons characteristic classes of vector bundles with a flat connecti
 on.\n\nOn a smooth projective variety over complex numbers\, Chern-Simons 
 classes of all flat bundles are torsion in degrees $>1$ by a theorem of Re
 znikov. Likewise\, $p$-adic characteristic classes on smooth varieties ove
 r an algebraically closed field of characteristic zero vanish (at least fo
 r $p$ large as compared to the rank of the local system) in degrees $>1$. 
 But for varieties over non-closed fields the characteristic classes of $p$
 -adic local systems turn out to often be non-zero even rationally. When $X
 $ is defined over a $p$-adic field\, characteristic classes of a $p$-adic 
 local system on it can be partially expressed in terms of Hodge-theoretic 
 invariants of the local system. This relation is established through consi
 dering an analog of Chern classes for vector bundles on the pro-étale sit
 e of $X$.\n\nThis is joint work with Lue Pan.\n
LOCATION:https://researchseminars.org/talk/MITNT/102/
END:VEVENT
END:VCALENDAR