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SUMMARY:Kate Finnerty (Boston University)
DTSTART:20251028T200000Z
DTEND:20251028T210000Z
DTSTAMP:20260422T173756Z
UID:FCNTS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FCNTS/10/">O
 n the possible adelic indices of certain families of elliptic curves</a>\n
 by Kate Finnerty (Boston University) as part of Five College Number Theory
  Seminar\n\nLecture held in Seeley Mudd 207 @Amherst College.\n\nAbstract\
 nA well-known theorem of Serre bounds the largest prime $\\ell$ for which 
 the mod $\\ell$ Galois representation of a non-CM elliptic curve $E/\\math
 bb{Q}$ is nonsurjective. Serre asked whether a universal bound on the larg
 est nonsurjective prime might exist. Significant partial progress has been
  made toward this question. Lemos proved that it has an affirmative answer
  for all $E$ admitting a rational cyclic isogeny. Zywina offered a more am
 bitious conjecture about the possible adelic indices that can occur as $E$
  varies. We will discuss a recent project (joint with Tyler Genao\, Jacob 
 Mayle\, and Rakvi) that extends Lemos's result to prove Zywina's conjectur
 e for certain families of elliptic curves.\n
LOCATION:https://researchseminars.org/talk/FCNTS/10/
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