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SUMMARY:Kate Finnerty (Boston University)
DTSTART:20251020T200000Z
DTEND:20251020T210000Z
DTSTAMP:20260423T040043Z
UID:NTBU/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTBU/31/">On
  the possible adelic indices of certain families of elliptic curves</a>\nb
 y Kate Finnerty (Boston University) as part of Boston University Number Th
 eory Seminar\n\nLecture held in CDS Room 548 in Boston University.\n\nAbst
 ract\nA well-known theorem of Serre bounds the largest prime $\\ell$ for w
 hich the mod $\\ell$ Galois representation of a non-CM elliptic curve $E/\
 \mathbb{Q}$ is nonsurjective. Serre asked whether a universal bound on the
  largest nonsurjective prime might exist. Significant partial progress has
  been made toward this question. Lemos proved that it has an affirmative a
 nswer for all $E$ admitting a rational cyclic isogeny. Zywina offered a mo
 re ambitious conjecture about the possible adelic indices that can occur a
 s $E$ varies. We will discuss an ongoing project (joint with Tyler Genao\,
  Jacob Mayle\, and Rakvi) that extends Lemos's result to prove Zywina's co
 njecture for certain families of elliptic curves.\n
LOCATION:https://researchseminars.org/talk/NTBU/31/
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