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
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.