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SUMMARY:Explicit surjectivity for Galois representations of products of el
 liptic curves over function fields [MPIM]
DTSTART:20250806T123000Z
DTEND:20250806T133000Z
DTSTAMP:20260721T133000Z
UID:indico-event-583@math-events.uni-bonn.de
DESCRIPTION:Speakers: Freddy Saia (University of Illinois at Chicago)\n\nN
 umber theory lunch seminar\nIt is natural to study the torsion of an ellip
 tic curve via its Galois representations\, which encode the action of Galo
 is on torsion points. Serre’s Open Image Theorem tells us that for an el
 liptic curve $E$ over a number field $F$\, the mod-$\\ell$ Galois represen
 tation is surjective for all sufficiently large primes $\\ell$. Since Serr
 e’s work\, considerable effort has gone towards obtaining extensions to 
 other classes of abelian varieties and also towards making “sufficiently
  large” effective.\nI will discuss joint work with Alina Cojocaru\, in w
 hich we obtain an explicit surjectivity result for products of elliptic cu
 rves over function fields. This comes from careful use of techniques of Ma
 sser—Wüstholz from the number field setting\, in combination with a res
 ult of Cojocaru—Hall for elliptic curves over function fields and recent
  isogeny bounds for elliptic curves over function fields due to Griffon—
 Pazuki. As an application\, we prove that most specializations of certain 
 families of products of elliptic curves over the rationals have no large e
 xceptional primes.\n \n\nhttps://math-events.uni-bonn.de/event/583/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/583/
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