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Sinnott's proof of Washington's theorem, and generalisations
If you have a question about this talk, please contact Joanna Fawcett.
In 1978 Washington proved that for any finite abelian extension k of the rationals, and any prime p, that if k(n) denotes the n-th layer of the cyclotomic Zp extension of k, then for all primes q different from p, the q-part of the ideal class group of k(n) stabilises as n tends to infinity. In 1987 Sinnott gave a beautiful proof of this theorem, which I shall discuss, and hopefully detail how one can generalise this proof to deduce results about Selmer groups of CM elliptic curves and ideal class groups over non-cyclotomic Zp extensions.
This talk is part of the Junior Algebra/Logic/Number Theory seminar series.
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