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

Location: A3.339
Organizer: 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).