Journal article
Cup products in the etale cohomology of number fields
New York journal of mathematics, Vol.24, pp.514-542
01/01/2018
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 integers n > 1, there are infinitely many number fields over which there are both trivial and non-trivial Kim invariants associated to cyclic groups of order n.
Details
- Title: Subtitle
- Cup products in the etale cohomology of number fields
- Creators
- F. M Bleher - Univ Iowa, Dept Math, Iowa City, IA 52242 USAT Chinburg - Univ Penn, Dept Math, Philadelphia, PA 19104 USAR GreenbergM Kakde - Kings Coll London, Dept Math, London WC2R 2LS, EnglandG Pappas - Michigan State UniversityM. J Taylor - Univ Oxford, Merton Coll, Oxford OX1 4JD, England
- Resource Type
- Journal article
- Publication Details
- New York journal of mathematics, Vol.24, pp.514-542
- Publisher
- ELECTRONIC JOURNALS PROJECT
- ISSN
- 1076-9803
- eISSN
- 1076-9803
- Number of pages
- 29
- Grant note
- CNS-1513671; CNS-1701785 / NSF SaTC Grants DMS-1360621; DMS-1265290; DMS-1360767; DMS-1360902; DMS-1360733 / NSF FRG Grant; National Science Foundation (NSF) 338379 / Simons Foundation Grant EP/L021986/1 / EPSRC First Grant; UK Research & Innovation (UKRI); Engineering & Physical Sciences Research Council (EPSRC) DMS-1801328; DMS-1701619; DMS-1107263/1107367/1107452 / NSF; National Science Foundation (NSF)
- Language
- English
- Date published
- 01/01/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984241041402771
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