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Colloquiums (FM & IMI)

A few thoughts on "index" in algebraic number theory [FM]

Hold Date
2010-11-18 16:00~2010-11-18 17:00
Lecture Room S-2, Faculty of Mathematics building, Ito Campus
Object person
Takashi ONO (Johns Hopkins University)

The talk belongs to a relatively new scenario in number theory.
Let K/k be a Galois extension of number fields. The main idea is to borrow
a method of Poincare on automorphic functions to do  number theory by
replacing the ring R of holomorphic functions on the upper half plane by the
ring of algebraic integers of K and the modular group G acting on R by the
Galois group of K/k.
It turns out that the  index of space of Poincare series in the  space of
modular forms ( for a given weight) corresponds to a kind of "index"
involving invariants in ramification theory of Galois extensions.