Research output: Contribution to journal › Article

Mahesh Ramesh Kakde, Frauke. M. Bleher, Ted Chinburg, Ralph Greenberg, George Pappas, Martin J. Taylor

Original language | English |
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Journal | New york journal of mathematics |

Accepted/In press | 12 Jul 2018 |

**Cup products in the_BLEHER_Accepted12July2018_GREEN AAM**CupProducts.pdf, 420 KB, application/pdf

Uploaded date:22 Aug 2018

Version:Accepted author manuscript

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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