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Duality for complexes of tori over a global field of positive characteristic

If K is a number field, arithmetic duality theorems for tori and complexes of tori over K are crucial to understand local-global principles for linear algebraic groups over K. When K is a global field of positive characteristic, we prove similar arithmetic duality theorems, including a Poitou-Tate exact sequence for Galois hypercohomology of complexes of tori. One of the main ingredients is Artin-Mazur-Milne duality theorem for fppf cohomology of finite flat commutative group schemes.

preprint2020arXivOpen access
Cyril DemarcheDavid Harari
math.AGmath.NT
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Cyril DemarcheDavid Harari

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