Thursday 13 Mar 2014Applications of hybrid p-adic group rings and hybrid Iwasawa algebras to arithmetic conjectures

Henri Johnston - Exeter

Harrison 103 15:00-16:00

We introduce the closely related notions of hybrid p-adic
group ring and hybrid Iwasawa algebra. When certain group-theoretic
criteria are met, hybrid p-adic group rings allow one to reduce the
proof of the equivariant Tamagawa number conjecture for a particular
Galois extension of number fields to the proofs of two easier
conjectures; this leads to unconditional proofs in certain cases. A
similar story holds for hybrid Iwasawa algebras and the equivariant
Iwasawa main conjecture for totally real fields, though there are some
important differences. This is joint work with Andreas Nickel

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