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SUMMARY:(A)typical intersections and where to find them - Gregorio Baldi (
 IHES)
DTSTART:20211019T133000Z
DTEND:20211019T143000Z
UID:TALK162196@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:I will present two seemingly unrelated results: (1) There exis
 ts a smooth projective curve C of genus 4\, defined over some number field
  K\, whose Jacobian 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)Th
 e Hodge locus of positive period dimension of the universal family of degr
 ee d hypersurfaces in \\mathbb{P}^{n+1} is algebraic as soon as n>2 and d>
 5. \n\nThe proof of both results builds on an ‘’Extended Zilber—Pink
  philosophy’’ for varieties supporting a variation of Hodge structure 
 which predicts the behaviour of typical and atypical intersections (whose 
 combination describes the whole Hodge locus). This is a joint work with B.
  Klingler and E. Ullmo.
LOCATION:Online
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