Exact sequences for the galois group

Abstract

When F C→ C is a monoidal functor between suitable symmetric closed categories and H is a finite commutative and cocbmmuta-ive Hopf algebra in C, we obtain, generalizing results of S. Qaeneppel and M. Beattie, two exact sequences involving the Picard, Galois and Brauer groups defined in [21], [11]. Finally we describe the relation between this exact sequences.

^*Partially supported by the European Community (Contract CHRX-CT93-0091).

^†Martially supported by the Universidad de Vigo ( Project 1427 ).

^*Partially supported by the European Community (Contract CHRX-CT93-0091).

^†Martially supported by the Universidad de Vigo ( Project 1427 ).

Notes

^*Partially supported by the European Community (Contract CHRX-CT93-0091).

^†Martially supported by the Universidad de Vigo ( Project 1427 ).