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SUMMARY:Gregorio Baldi (IMJ and IAS)
DTSTART:20260414T210000Z
DTEND:20260414T220000Z
DTSTAMP:20260419T151149Z
UID:BC-MIT/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BC-MIT/34/">
 Intersections and the Bézout Range for Abelian Varieties</a>\nby Gregorio
  Baldi (IMJ and IAS) as part of BC-MIT number theory seminar\n\nLecture he
 ld in 2-449 at MIT.\n\nAbstract\nGiven subvarieties X\,Y of a complex alge
 braic variety S of complementary dimension\, must they intersect? When S i
 s projective space\, this is a consequence of the classical Bézout theore
 m\, and an analogue for simple abelian varieties was established by Barth 
 in 1968. Moreover\, the moving lemma suggests that\, after suitable transl
 ations\, one may arrange for intersections of the expected dimension.\nIn 
 this talk\, we describe variants for simple abelian varieties in the spiri
 t of the completed Zilber--Pink philosophy. When X and Y have complementar
 y dimension\, we show that the intersections X∩[n]Y are zero-dimensional
  for all but finitely many integers n\, and that these intersections colle
 ctively give rise to an analytically dense subset of X as n varies. We mor
 eover control those n for which X∩[n]Y has a positive dimensional compon
 ent uniformly in X\,Y and A. When dimX+dimY < dim A\, we show that X∩[n]
 Y=∅ for a set of integers n of asymptotic density one\, except in the pr
 esence of intersections at torsion points.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/34/
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