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Mathematics > Number Theory

arXiv:2210.01396 (math)
[Submitted on 4 Oct 2022 (v1), last revised 2 Aug 2023 (this version, v4)]

Title:Class field theory, Hasse principles and Picard-Brauer duality for two-dimensional local rings

Authors:Takashi Suzuki
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Abstract:We draw concrete consequences from our arithmetic duality for two-dimensional local rings with perfect residue field. These consequences include class field theory, Hasse principles for coverings and $K_{2}$ and a duality between divisor class groups and Brauer groups. To obtain these, we analyze the ind-pro-algebraic group structures on arithmetic cohomology obtained earlier and prove some finiteness properties about them.
Comments: Accepted for publication in Algebraic Geometry. No changes in the text from v3. 48 pages
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
MSC classes: 11G45 (Primary) 14F20, 19F05, 11S25 (Secondary)
Cite as: arXiv:2210.01396 [math.NT]
  (or arXiv:2210.01396v4 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.2210.01396
Journal reference: Algebraic Geometry 11 (4) (2024) 460--505
Related DOI: https://doi.org/10.14231/AG-2024-015

Submission history

From: Takashi Suzuki [view email]
[v1] Tue, 4 Oct 2022 06:09:10 UTC (42 KB)
[v2] Thu, 13 Oct 2022 09:48:26 UTC (43 KB)
[v3] Tue, 1 Aug 2023 06:58:07 UTC (43 KB)
[v4] Wed, 2 Aug 2023 06:51:35 UTC (43 KB)
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