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SUMMARY:Heidi Goodson (Brooklyn College (CUNY))
DTSTART:20221129T210000Z
DTEND:20221129T220000Z
DTSTAMP:20260423T010102Z
UID:UAANTS/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/52/">
 Degeneracy and Sato-Tate Groups in Dimension Greater than 3</a>\nby Heidi 
 Goodson (Brooklyn College (CUNY)) as part of University of Arizona Algebra
  and Number Theory Seminar\n\n\nAbstract\nThe term degenerate is used to d
 escribe abelian varieties whose Hodge rings contain exceptional cycles -- 
 Hodge cycles that are not generated by divisor classes. We can see the eff
 ect of the exceptional cycles on the structure of an abelian variety throu
 gh its Mumford-Tate group\, Hodge group\, and Sato-Tate group. In this tal
 k I will discuss degeneracy through these different but related lenses\, s
 pecializing to Jacobians of hyperelliptic curves of the form $y^2=x^m−1$
 . Together\, we will explore the various forms of degeneracy for several e
 xamples\, each illustrating different phenomena that can occur.\n
LOCATION:https://researchseminars.org/talk/UAANTS/52/
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