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SUMMARY:Alexander Petrov (Harvard)
DTSTART:20220419T203000Z
DTEND:20220419T213000Z
DTSTAMP:20260423T125215Z
UID:MITNT/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/48/">G
 alois action on the pro-algebraic fundamental group</a>\nby Alexander Petr
 ov (Harvard) as part of MIT number theory seminar\n\nLecture held in Room 
 2-449 in the Simons Building (building 2).\n\nAbstract\nGiven a smooth var
 iety X over a number field\, the action of the Galois group on the geometr
 ic etale fundamental group of X makes the ring of functions on the pro-alg
 ebraic completion of this fundamental group into a (usually infinite-dimen
 sional) Galois representation. This Galois representation turns out to sat
 isfy the following two properties:\n\n1)Every finite-dimensional subrepres
 entation of it satisfies the assumptions of the Fontaine-Mazur conjecture:
  it is de Rham an almost everywhere unramifed.\n\n2)If X is the projective
  line with three punctures\, the semi-simplification of every Galois repre
 sentation of geometric origin is a subquotient of the ring of regular func
 tions on the pro-algebraic completion of the etale fundamental group of X.
 \n\nI will also discuss a conjectural characterization of local systems of
  geometric origin on complex algebraic varieties\, arising from property 1
 ) above.\n
LOCATION:https://researchseminars.org/talk/MITNT/48/
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