Arithmetic Duality
Number Theory
2025-12-03 v2 Algebraic Geometry
Abstract
In the 1950s and 1960s Tate proved some duality theorems in the Galois cohomology of finite modules and abelian varieties. As for most of Tate's work this has had a profound influence on mathematics with many applications and further developments. In this article, I discuss Tate's theorems and some of these developments.
Keywords
Cite
@article{arxiv.2509.13016,
title = {Arithmetic Duality},
author = {James S. Milne},
journal= {arXiv preprint arXiv:2509.13016},
year = {2025}
}
Comments
21 pages. This is the written version of my talk at the conference, The Legacy of John Tate, and Beyond. Harvard University, March 17, 2025. v2. 23 pages, many small improvements to the exposition