TL;DR
This paper revisits Tate's theory of augmented cup products in profinite cohomology, providing a modern constructive perspective and linking it to pairings in algebraic geometry.
Contribution
It offers a modern constructive interpretation of Tate's augmented cup products and connects them to pairings between groups related to algebraic curves.
Findings
Reformulation of Tate's augmented cup products in a modern constructive framework
Interpretation of pairings between groups associated to curves via augmented cup products
Bridging cohomological theory with algebraic geometry applications
Abstract
In this paper, we present Tate's theory of augmented cup products in profinite cohomology in a modern constructive style. As an application, we interpret pairings between groups associated to curves constructed by Lichtenbaum, in terms of augmented cup products.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology