Ober­se­mi­nar "Num­ber Theo­ry and Arith­me­ti­cal Sta­ti­stics": Dr. Béran­ger Se­gu­in (Pa­der­born), Coun­ting ex­ten­si­ons of di­vi­si­on al­ge­bras over num­ber fields

Ort: A3.339
Veranstalter: Prof. Dr. Jürgen Klüners

Titel: Counting extensions of division algebras over number fields (joint work with Fabian Gundlach)

Abstract: We present and explain the proof of results concerning the asymptotical density of discriminants of extensions of a given division algebra over a number field.
This is an extension of the question of the distribution of number fields to the case of non-commutative fields.
We explain what happens both in the case of "inner Galois extensions" (analogous to central simple algebras over a commutative field) and "outer Galois extensions" (analogous to ordinary Galois extensions of a commutative field).