Class Groups in Cyclic p - Extensions of Number Fields

Friday, November 9, 2012 at 1:00pm to 1:45pm

Bronfman Science Center, 106 18 Hoxsey St, Williamstown, MA 01267, USA

Class Groups in Cyclic p - Extensions of Number FieldsProf. Michael Rosen, Brown University
Mathematics and Statistics Department Faculty Seminar

Abstract: Let E/F be a cyclic extension of number fields of degree p^n, where p is a prime. It is proved that the p rank of the class group of E is bounded by p^n (t-1+rk_{p}Cl_F) where t is the number of primes in F which ramify in E. All terms will be explained. This result generalizes in various ways an old result of Gary Cornell. We will also discuss the more general case where the Galois group of E/F is abelian.

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Mathematics & Statistics

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