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  Tensor triangular geometry of filtered objects and sheaves

Aoki, K. (2023). Tensor triangular geometry of filtered objects and sheaves. Mathematische Zeitschrift, 303: 62. doi:10.1007/s00209-023-03210-z.

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2001.00319.pdf (Preprint), 493KB
 
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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

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Aoki, Ko1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Topology, Algebraic Geometry, Category Theory
 Abstract: We compute the Balmer spectra of compact objects of tensor triangulated categories whose objects are filtered or graded objects of (or sheaves valued in) another tensor triangulated category. Notable examples include the filtered derived category of a scheme as well as the homotopy category of filtered spectra. We use an ∞-categorical method to properly formulate and deal with the problem. Our computations are based on a point-free approach, so that distributive lattices and semilattices are used as key tools. In the Appendix, we prove that the ∞-topos of hypercomplete sheaves on an ∞-site is recovered from a basis, which may be of independent interest.

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Language(s): eng - English
 Dates: 2023
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: arXiv: 2001.00319
DOI: 10.1007/s00209-023-03210-z
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Title: Mathematische Zeitschrift
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 303 Sequence Number: 62 Start / End Page: - Identifier: -