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SUMMARY:Pseudorepresentations and the Eisenstein ideal - Carl Wang Erickso
 n (Imperial College)
DTSTART:20170530T130000Z
DTEND:20170530T140000Z
UID:TALK72483@talks.cam.ac.uk
CONTACT:G. Rosso
DESCRIPTION:In his landmark 1976 paper "Modular curves and the Eisenstein 
 ideal"\, Mazur studied congruences modulo p between cusp forms and an Eise
 nstein series of weight 2 and prime level N. He proved a great deal about 
 these congruences\, but also posed a number of questions: how big is the s
 pace of cusp forms that are congruent to the Eisenstein series? How big is
  the extension generated by their coefficients? In joint work with Preston
  Wake\, we give an answer to these questions using the deformation theory 
 of Galois pseudorepresentations. The answer is intimately related to the a
 lgebraic number theoretic interactions between the primes N and p\, and is
  given in terms of cup products (and Massey products) in Galois cohomology
 .
LOCATION:MR13
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