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CATEGORIES:Number Theory Seminar
SUMMARY:Pseudorepresentations and the Eisenstein ideal - C
arl Wang Erickson (Imperial College)
DTSTART;TZID=Europe/London:20170530T140000
DTEND;TZID=Europe/London:20170530T150000
UID:TALK72483AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72483
DESCRIPTION:In his landmark 1976 paper "Modular curves and the
Eisenstein ideal"\, Mazur studied congruences mod
ulo p between cusp forms and an Eisenstein series
of weight 2 and prime level N. He proved a great d
eal about these congruences\, but also posed a num
ber of questions: how big is the space of cusp for
ms that are congruent to the Eisenstein series? Ho
w big is the extension generated by their coeffici
ents? In joint work with Preston Wake\, we give an
answer to these questions using the deformation t
heory of Galois pseudorepresentations. The answer
is intimately related to the algebraic number theo
retic interactions between the primes N and p\, an
d is given in terms of cup products (and Massey pr
oducts) in Galois cohomology.
LOCATION:MR13
CONTACT:G. Rosso
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