BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Arvind Suresh (U of Arizona)
DTSTART:20230418T210000Z
DTEND:20230418T220000Z
DTSTAMP:20260423T041613Z
UID:UAANTS/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/65/">
 Realizing Galois representations in abelian varieties by specialization</a
 >\nby Arvind Suresh (U of Arizona) as part of University of Arizona Algebr
 a and Number Theory Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nWe 
 present a strategy for constructing abelian varieties J/K which realize a 
 given rational Galois representation $\\rho : G_K \\to GL_n(Q)$\, i.e. suc
 h that $\\rho$ is a subrep of $J(\\Kbar)\\otimes \\Q$. When $\\rho$ is the
  trivial rep.\, then $J/K$ realizes $\\rho$ if and only if $J(K)$ is of ra
 nk at least $n$\, and such families are usually constructed by the special
 ization method pioneered by Neron. Our strategy consists in taking an alre
 ady existing construction of abelian varieties with large rank and\, provi
 ded there is enough symmetry\, twisting the construction to obtain non-tri
 vial Galois actions on the points. After twisting\, we use a simple genera
 lization of the classical Neron specialization theorem (from trivial reps.
  to non-trivial reps.) We apply this procedure to a construction of Mestre
  and Shioda to prove the following: Given a representation $\\rho: G_K \\t
 o GL_n(\\Q)$\, there exist infinitely many absolutely simple absolutely ab
 elian varieties $J/K$ (which are in fact Jacobians of hyperelliptic curves
 ) such that $\\rho$ is a subrep. of the $G_K$ rep on $J(\\Kbar) \\otimes_{
 \\Z} \\Q$.\n
LOCATION:https://researchseminars.org/talk/UAANTS/65/
END:VEVENT
END:VCALENDAR