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CATEGORIES:Number Theory Seminar
SUMMARY:(A)typical intersections and where to find them -
Gregorio Baldi (IHES)
DTSTART;TZID=Europe/London:20211019T143000
DTEND;TZID=Europe/London:20211019T153000
UID:TALK162196AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/162196
DESCRIPTION:I will present two seemingly unrelated results: (1
) There exists a smooth projective curve C of genu
s 4\, defined over some number field K\, whose Jac
obian J satisfies: End(J)=\\Z and the image of the
absolute Galois group of K in End(T_\\ell (J)) is
not open in GSp_8(Z_\\ell). (2)The Hodge locus of
positive period dimension of the universal family
of degree d hypersurfaces in \\mathbb{P}^{n+1} is
algebraic as soon as n>2 and d>5. \n\nThe proof o
f both results builds on an ‘’Extended Zilber—Pink
philosophy’’ for varieties supporting a variation
of Hodge structure which predicts the behaviour o
f typical and atypical intersections (whose combin
ation describes the whole Hodge locus). This is a
joint work with B. Klingler and E. Ullmo.
LOCATION:Online
CONTACT:Rong Zhou
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