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SUMMARY:Prismatic $F$-gauges
DTSTART;VALUE=DATE-TIME:20230110T103000Z
DTEND;VALUE=DATE-TIME:20230110T113000Z
DTSTAMP;VALUE=DATE-TIME:20241005T164858Z
UID:indico-event-8742@cern.ch
DESCRIPTION:Abstract: Prismatic $F$-gauges are the natural coefficient sys
tems for prismatic cohomology\, analogous to variations\nof Hodge structur
es in classical Hodge theory. In this talk\, I will explain what they are\
, and why understanding them for\n$\\mathrm{Spf}(\\mathbf{Z}_p)$ itself ca
n be useful in both geometry and arithmetic. \n\nIn geometry\, we shall de
scribe Drinfeld's recent proof of (a refinement of) the Deligne--Illusie t
heorem for algebraic de Rham cohomology in characteristic $p$. \n\nIn arit
hmetic\, we shall explain how $F$-gauges yield a meaningful notion of crys
tallinity for integral/torsion representations of the absolute Galois grou
p of $\\mathbf{Q}_p$\; the cohomology of $F$-gauges then gives an analog o
f the local Bloch--Kato Selmer groups for such representations with favora
ble properties (e.g.\, it interacts quite well with (a refinement of) the
local Tate duality theorem).\n\nThis is joint work in progress with Jacob
Lurie\, building on work of Drinfeld.\n\nhttps://indico.tifr.res.in/indico
/conferenceDisplay.py?confId=8742
LOCATION: AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8742
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