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SUMMARY:A Chabauty-Coleman bound for surfaces in Abelian Varieties
DTSTART;VALUE=DATE-TIME:20220505T120000Z
DTEND;VALUE=DATE-TIME:20220505T130000Z
DTSTAMP;VALUE=DATE-TIME:20220815T065704Z
UID:indico-event-7790@indico.math.cnrs.fr
DESCRIPTION:Coleman's explicit version of Chabauty's p-adic approach to Mo
rdell's conjecture gives a concrete bound for the number of rational point
s of a curve C of genus g >1 over the rationals\, provided that the rank o
f its Jacobian is r< g. Namely\, if p >2g is a prime of good reduction for
C\, the number of rational points of C is bounded by the number of mod-p
points of C plus a contribution coming from the canonical sheaf of C. \n\
nThere have been several striking developments around this result\, but at
present such a precise bound has remained out of reach for higher dimensi
onal varieties. In this talk we will outline the proof of an analogous res
ult for surfaces of general type contained in abelian varieties of Mordell
-Weil rank 0 or 1\, under some assumptions on the reduction type at p. For
this\, we develop a method based on overdetermined w-integrality in posit
ive characteristic. This is joint work with Hector Pasten.\n\nhttps://indi
co.math.cnrs.fr/event/7790/
LOCATION:ENS Lyon\, UMPA M7.411
URL:https://indico.math.cnrs.fr/event/7790/
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