2023/05/15 by Cristian D. González-Avilés, Gonzalez-Aviles, Cristian D. · 1 citation
Mathematics · #11G25 #14G20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2305.08699
openalex publication_date 2023/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If k is an arbitrary field, we construct a category of k-1-motives in which every commutative algebraic k-group G has a dual object G\vee. When k is a local field of arbitrary characteristic, we establish Pontryagin duality theorems that relate the fppf cohomology groups of G to the hypercohomology groups of the k-1-motive G\vee. We also obtain a duality theorem for the second cohomology group of an arbitrary k-1-motive. These results have applications (to be discussed elsewhere) to certain extensions of Lichtenbaum-van Hamel duality to a class of non-smooth proper k-varieties.