Number Theory Seminar

Daniel Smertnig, Department of Pure Mathematics, University of Waterloo

"On basic and Bass quaternion orders"

Quaternion orders can possess many different ring-theoretical properties, such as being maximal, hereditary, Eichler, Bass, or Gorenstein. I will recall these properties and their relations to each other, summarizing a 'taxonomy' of quaternion orders. A quaternion order O over a domain R is basic if it contains an integrally closed quadratic R-order. I will show that a quaternion order is Bass if and only if it is basic, in the local and global settings.

This is joint work with Sara Chari and John Voight.

MC 5417