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

2020/01/28 by Cyril Demarche, Demarche, Cyril, David Harari +1
Mathematics · #11E72 #11G20 #14F20 #14H25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2001.10236

openalex publication_date 2020/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If K is a number field, arithmetic duality theorems for tori and complexes of\ntori over K are crucial to understand local-global principles for linear\nalgebraic groups over K. When K is a global field of positive characteristic,\nwe prove similar arithmetic duality theorems, including a Poitou-Tate exact\nsequence for Galois hypercohomology of complexes of tori. One of the main\ningredients is Artin-Mazur-Milne duality theorem for fppf cohomology of finite\nflat commutative group schemes.\n

Citations

• Algebraic Groups Over Finite Fields

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