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Cup products in the etale cohomology of number fields

Research output: Working paperPre-print

Mahesh Ramesh Kakde, F. M. Bleher, Ralph Greenberg, T. Chinburg, G Pappas, Martin J. Taylor

Original languageEnglish
Publication statusUnpublished - 19 May 2017

Bibliographical note

https://arxiv.org/abs/1705.07110

King's Authors

Abstract

This paper concerns cup product pairings in \'etale cohomology related to work of M. Kim and of W. McCallum and R. Sharifi. We will show that by considering Ext groups rather than cohomology groups, one arrives at a pairing which combines invariants defined by Kim with a pairing defined by McCallum and Sharifi. We also prove a formula for Kim's invariant in terms of Artin maps in the case of cyclic unramified Kummer extensions. One consequence is that for all n>1, there are infinitely many number fields F over which there are both trivial and non-trivial Kim invariants associated to cyclic groups of order n.

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