Cup products in the etale cohomology of number fields

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

Cup products in the etale cohomology of number fields

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

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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.

Original language	English
Journal	New york journal of mathematics
Publication status	Accepted/In press - 12 Jul 2018

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title = "Cup products in the etale cohomology of number fields",

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.",

author = "Kakde, {Mahesh Ramesh} and Bleher, {Frauke. M.} and Ted Chinburg and Ralph Greenberg and George Pappas and Taylor, {Martin J.}",

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language = "English",

journal = "New york journal of mathematics",

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AU - Kakde, Mahesh Ramesh

AU - Bleher, Frauke. M.

AU - Chinburg, Ted

AU - Greenberg, Ralph

AU - Pappas, George

AU - Taylor, Martin J.

PY - 2018/7/12

Y1 - 2018/7/12

N2 - 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.

AB - 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.

M3 - Article

SN - 1076-9803

JO - New york journal of mathematics

JF - New york journal of mathematics

ER -

Cup products in the etale cohomology of number fields

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