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SUMMARY:Kate Finnerty (Boston University)
DTSTART:20251028T200000Z
DTEND:20251028T210000Z
DTSTAMP:20260824T074833Z
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 Pioneer Valley Number Theo
 ry Seminar\n\nLecture held in Seeley Mudd 207 @Amherst College.\n\nAbstrac
 t\nA well-known theorem of Serre bounds the largest prime $\\ell$ for whic
 h the mod $\\ell$ Galois representation of a non-CM elliptic curve $E/\\ma
 thbb{Q}$ is nonsurjective. Serre asked whether a universal bound on the la
 rgest nonsurjective prime might exist. Significant partial progress has be
 en made toward this question. Lemos proved that it has an affirmative answ
 er for all $E$ admitting a rational cyclic isogeny. Zywina offered a more 
 ambitious conjecture about the possible adelic indices that can occur as $
 E$ varies. We will discuss a recent project (joint with Tyler Genao\, Jaco
 b Mayle\, and Rakvi) that extends Lemos's result to prove Zywina's conject
 ure for certain families of elliptic curves.\n
LOCATION:https://researchseminars.org/talk/FCNTS/10/
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