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SUMMARY:Andrew Sutherland (MIT)
DTSTART:20221014T124000Z
DTEND:20221014T134000Z
DTSTAMP:20260423T021249Z
UID:OBAGS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OBAGS/10/">S
 ato-Tate groups of abelian varieties</a>\nby Andrew Sutherland (MIT) as pa
 rt of ODTU-Bilkent Algebraic Geometry Seminars\n\nLecture held in ODTÜ Ma
 thematics department Room M-203.\n\nAbstract\nLet A be an abelian variety 
 of dimension g defined over a number field K.  As defined by Serre\, the S
 ato-Tate group ST(A) is a compact subgroup of the unitary symplectic group
  USp(2g) equipped with a map that sends each Frobenius element of the abso
 lute Galois group of K at primes p of good reduction for A to a conjugacy 
 class of ST(A) whose characteristic polynomial is determined by the zeta f
 unction of the reduction of A at p.  Under a set of axioms proposed by Ser
 re that are known to hold for g <= 3\, up to conjugacy in Usp(2g) there is
  a finite list of possible Sato-Tate groups that can arise for abelian var
 ieties of dimension g over number fields.  Under the Sato-Tate conjecture 
 (which is known for g=1 when K has degree 1 or 2)\, the asymptotic distrib
 ution of normalized Frobenius elements is controlled by the Haar measure o
 f the Sato-Tate group.\n\nIn this talk I will present a complete classific
 ation of the Sato-Tate groups that can and do arise for g <= 3.\n\nThis is
  joint work with Francesc Fite and Kiran Kedlaya.\n\nThis is a hybrid talk
 . To request Zoom link please write to sertoz@bilkent.edu.tr\n
LOCATION:https://researchseminars.org/talk/OBAGS/10/
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