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SUMMARY:Jeff Achter (Colorado State University)
DTSTART:20250923T203000Z
DTEND:20250923T213000Z
DTSTAMP:20260423T130433Z
UID:MITNT/120
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/120/">
 Torsion finite problems</a>\nby Jeff Achter (Colorado State University) as
  part of MIT number theory seminar\n\nLecture held in Room 2-449 in the Si
 mons Building (building 2).\n\nAbstract\nConsider an abelian variety A ove
 r a number field K.  The torsion\nsubgroup of A(K) is finite\; a result of
  Ribet shows that this finiteness\npersists over the cyclotomic extension 
 of K.\n\nNow consider a second abelian variety B/K\, and the infinite exte
 nsion\nK_B generated by the coordinates of its torsion points.  Conditiona
 l\non the Mumford-Tate conjecture (and up to a finite extension of K)\,\nI
  will give a criterion for the finitude of the torsion subgroup of\nA(K_B)
 .  I'll also describe a motivic generalization of\nthis story\, which in r
 etrospect explains  certain\nalgebraic cycles we discovered on torsion-inf
 inite pairs of CM abelian\nvarieties. (Joint work with Lian Duan and Xiyua
 n Wang.)\n
LOCATION:https://researchseminars.org/talk/MITNT/120/
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