Soit un espace homogène d’un groupe réductif à stabilisateurs réductifs, défini sur un corps global de caractéristique positive. À l’aide de théorèmes de dualité pour les complexes de tores, on étudie les obstructions cohomologiques naturelles à différentes propriétés arithmétiques.
Let be a homogeneous space of a reductive group with reductive stabilizers, defined over a global field of positive characteristic. Using duality theorems for complexes of tori, we study cohomological obstructions to various arithmetic properties.
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Mots clés : Global function fields, Hasse principle, Weak and Strong approximation, Brauer–Manin obstruction, algebraic groups, homogeneous spaces
@article{AHL_2022__5__1111_0, author = {Demarche, Cyril and Harari, David}, title = {Local-global principles for homogeneous spaces of reductive groups over global function fields}, journal = {Annales Henri Lebesgue}, pages = {1111--1149}, publisher = {\'ENS Rennes}, volume = {5}, year = {2022}, doi = {10.5802/ahl.144}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ahl.144/} }
TY - JOUR AU - Demarche, Cyril AU - Harari, David TI - Local-global principles for homogeneous spaces of reductive groups over global function fields JO - Annales Henri Lebesgue PY - 2022 SP - 1111 EP - 1149 VL - 5 PB - ÉNS Rennes UR - http://www.numdam.org/articles/10.5802/ahl.144/ DO - 10.5802/ahl.144 LA - en ID - AHL_2022__5__1111_0 ER -
%0 Journal Article %A Demarche, Cyril %A Harari, David %T Local-global principles for homogeneous spaces of reductive groups over global function fields %J Annales Henri Lebesgue %D 2022 %P 1111-1149 %V 5 %I ÉNS Rennes %U http://www.numdam.org/articles/10.5802/ahl.144/ %R 10.5802/ahl.144 %G en %F AHL_2022__5__1111_0
Demarche, Cyril; Harari, David. Local-global principles for homogeneous spaces of reductive groups over global function fields. Annales Henri Lebesgue, Tome 5 (2022), pp. 1111-1149. doi : 10.5802/ahl.144. http://www.numdam.org/articles/10.5802/ahl.144/
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