Arithmetic Duality Theorems for 1-Motives

Details Arithmetic Duality Theorems for 1-Motives Arithmetic Duality Theorems for 1-Motives

2003-04-29

arxiv.org/abs/math/0304480v3

Mathematics

Number Theory

44 pages, LaTeX, final version. Section 5 substantially rewritten

Scientific paper

We prove several duality theorems for the Galois and etale cohomology of
1-motives defined over local and global fields and establish a 12-term
Poitou-Tate type exact sequence. The results give a common generalisation and
sharpening of well-known theorems by Tate on abelian varieties as well as
results by Tate/Nakayama and Kottwitz on algebraic tori.

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