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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).