Thursday 22 Nov 2018: NT Seminar: Computing isomorphisms between lattices
Dr. Henri Johnston - University of Exeter
Let K be a number field, let A be a finite dimensional semisimple K-algebra and let Lambda be an O_K-order in A. In particular, for a finite G group, one can take A=Q[G] and Lambda=Z[G]. In this talk, we shall describe an algorithm that, under certain hypotheses on A, for two given Lambda-lattices X and Y either computes an isomorphism X -> Y or determines that X and Y are not isomorphic. This algorithm has can be used to investigate questions concerning the Galois module structure of rings of integers and ambiguous ideals of tamely ramified Galois extensions of Q. This is joint work with Tommy Hofmann (Kaiserslautern).