Weil- 'etale cohomology and duality for arithmetic schemes in negative\n weights

2020/12/20 by Alexey Beshenov, Beshenov, Alexey
Mathematics · #14F20 #14F42 #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.2012.11034

openalex publication_date 2020/12/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Flach and Morin constructed in (Doc. Math. 23 (2018), 1425--1560)\nWeil- 'etale cohomology Hⁱ_\W,c (X, \ℤ (n)) for a proper,\nregular arithmetic scheme X (i.e. separated and of finite type over\n\Spec \ℤ) and n \∈ \ℤ. In the case when n <\n0, we generalize their construction to an arbitrary arithmetic scheme X,\nthus removing the proper and regular assumption. The construction assumes\nfinite generation of suitable 'etale motivic cohomology groups.\n

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