Abstract
Tate sequences are an important tool for tackling problems related to the (ill-understood) Galois structure of groups of S-units. The relatively recent Tate sequence “for small S” of Ritter and Weiss allows one to use the sequence without assuming the vanishing of the S-class-group, a significant advance in the theory. Associated to Ritter and Weiss’s version of the sequence are connecting homomorphisms in Tate cohomology, involving the S-class-group, that do not exist in the earlier theory. In the present article, we give explicit descriptions of certain of these connecting homomorphisms under some assumptions on the set S. 2000 Mathematics Subject Classification: Primary 11R29; Secondary 11R34.
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