Wilhelm Killing Kolloquium: Prof. Dr. Jean-Pierre Tignol (UCLouvain): Linkage of quaternion algebras and systems of quadratic equations over number fields

Thursday, 27.04.2023 14:15 im Raum M4

Mathematik und Informatik

Lecture in Memoriam W. Scharlau - In the early development stages of the algebraic theory of quadratic forms, the following property was discussed: two quaternion algebras over a field are said to be linked if they contain pure quaternions whose squares are equal. The celebrated Hasse-Minkowski theorem shows that any two quaternion algebras over a number field are linked. This talk will explore how far this property extends to more than two quaternion algebras over various fields. In particular, as a result of a joint work with Adam Chapman (Annals of K-theory, 2019), we will exhibit four quaternion algebras over the field of rational functions in two variables over the complex numbers that are not linked. The proof uses reduction of a system of quadratic equations modulo 2.

Angelegt am Friday, 24.02.2023 12:53 von cauri_01
Geändert am Monday, 06.03.2023 11:20 von cauri_01
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Vorträge des SFB 1442
Kolloquium Wilhelm Killing