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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
- Place
- Lecture Room S-2, Faculty of Mathematics building, Ito Campus
- Object person
- Speaker
- Takashi ONO (Johns Hopkins University)

summary:

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.