Duality for complexes of tori over a global field of positive characteristic
Journal de l’École polytechnique — Mathématiques, Volume 7 (2020), pp. 831-870.

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 the Artin-Mazur-Milne duality theorem for fppf cohomology of finite flat commutative group schemes.

Sur un corps de nombres K, les théorèmes de dualité pour les tores et les complexes de tores sont cruciaux afin de comprendre le principe local-global pour les K-groupes algébriques linéaires. Nous démontrons de tels théorèmes de dualité arithmétique quand K est un corps global de caractéristique p, et en particulier nous établissons une suite de Poitou-Tate pour l’hypercohomologie galoisienne d’un complexe de tores. Un des principaux ingrédients est la dualité d’Artin-Mazur-Milne pour la cohomologie fppf d’un schéma en groupes fini et plat.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.129
Classification: 11E72,  11G20,  14F20,  14H25
Keywords: Artin-Mazur-Milne duality, complex of tori, flat cohomology, Poitou-Tate exact sequence
Cyril Demarche 1; David Harari 2

1 Université de Paris, Sorbonne Université, CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche 75013 Paris, France and Département de mathématiques et applications, École normale supérieure, CNRS, PSL Research University 45 rue d’Ulm, 75005 Paris, France
2 Université Paris-Saclay, C.N.R.S., Laboratoire de Mathématiques d’Orsay 91405 Orsay, France
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Cyril Demarche; David Harari. Duality for complexes of tori over a global field of positive characteristic. Journal de l’École polytechnique — Mathématiques, Volume 7 (2020), pp. 831-870. doi : 10.5802/jep.129. https://jep.centre-mersenne.org/articles/10.5802/jep.129/

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