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SUMMARY:Hélène Esnault (FU Berlin)
DTSTART:20210415T150000Z
DTEND:20210415T162000Z
DTSTAMP:20260423T035748Z
UID:RAMpAGe/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/41/"
 >Connections and Symmetric Differential Forms</a>\nby Hélène Esnault (FU
  Berlin) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\
 n\nAbstract\n(work in progress with Michael Groechenig)\nIf $X$ is smooth 
 complex projective and does not have any non-trivial symmetric differentia
 l forms\, then all its complex local systems have finite monodromy (Bruneb
 arbe-Klingler-Totaro ’13\, in answer to a question I had posed). The pro
 of relies on positivity theory stemming from Hodge Theory.\n\nThe aim is t
 o understand a suitable formulation in characteristic $p>0$.\n\nIf $X$ is 
 smooth projective over  the algebraic closure $k$ of  finite field\, and d
 oes not have non-trivial differential forms\, one may ask whether all conv
 ergent isocrystals have finite monodromy. This is true if $X$ lifts to $W(
 k)$. If $X$ lifts to $W_2(k)$\,  one can show that stable rank $2$ connect
 ions of degree $0$ have finite monodromy (i.e. are trivializable by a fini
 te étale cover).\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/41/
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