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SUMMARY:Levent Alpöge (Harvard)
DTSTART:20211116T213000Z
DTEND:20211116T223000Z
DTSTAMP:20260423T125533Z
UID:MITNT/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/39/">A
  "height-free" effective isogeny estimate for abelian varieties of $\\GL_2
 $-type.</a>\nby Levent Alpöge (Harvard) as part of MIT number theory semi
 nar\n\nLecture held in Room 2-143 in the Simons building.\n\nAbstract\nLet
  $g\\in \\mathbb{Z}^+$\, $K$ a number field\, $S$ a finite set of places o
 f $K$\, and $A\,B/K$ $g$-dimensional abelian varieties with good reduction
  outside $S$ which are $K$-isogenous and of $\\GL_2$-type over $\\overline
 {\\mathbb{Q}}$. We show that there is a $K$-isogeny $A\\rightarrow B$ of d
 egree effectively bounded in terms of $g$\, $K$\, and $S$ only.\n\nWe dedu
 ce among other things an effective upper bound on the number of $S$-integr
 al $K$-points on a Hilbert modular variety.\n
LOCATION:https://researchseminars.org/talk/MITNT/39/
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