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SUMMARY:Victoria Cantoral
DTSTART:20200727T163000Z
DTEND:20200727T170000Z
DTSTAMP:20260423T035935Z
UID:POINT/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINT/1/">Th
 e Mumford—Tate conjecture implies the algebraic Sato—Tate conjecture</
 a>\nby Victoria Cantoral as part of POINT: New Developments in Number Theo
 ry\n\n\nAbstract\nThe famous Mumford-Tate conjecture asserts that\, for ev
 ery prime number $\\ell$\, Hodge cycles are $\\mathbb{Q}_{\\ell}$-linear c
 ombinations of Tate cycles\, through Artin's comparisons theorems between 
 Betti and étale cohomology. The algebraic Sato-Tate conjecture\, introduc
 ed by Serre and developed later by Banaszak and Kedlaya\, is a powerful to
 ol in order to prove new instances of the generalized Sato-Tate conjecture
 . This previous conjecture is related with the equidistribution of Frobeni
 us traces.\n\nOur main goal is to prove that the Mumford-Tate conjecture f
 or an abelian variety A implies the algebraic Sato-Tate conjecture for A. 
 The relevance of this result lies mainly in the fact that the list of know
 n cases of the Mumford-Tate conjecture was up to now a lot longer than the
  list of known cases of the algebraic Sato-Tate conjecture. This is a join
 t work with Johan Commelin.\n\nIf you like to attend the talk\, please reg
 ister here: https://umich.zoom.us/meeting/register/tJAufuqtqDksG9fEmjTbWHM
 4QOEUad6Ke-DE.\n
LOCATION:https://researchseminars.org/talk/POINT/1/
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