The homotopy category of flat modules, and Grothendieck duality

Amnon Neeman

doi:10.1007/s00222-008-0131-0

The homotopy category of flat modules, and Grothendieck duality

Amnon Neeman^*

^*Corresponding author for this work

Research output: Contribution to journal › Review article › peer-review

129 Citations (Scopus)

Abstract

Let R be a ring. We prove that the homotopy category K(R-Proj) is always א₁-compactly generated, and, depending on the ring R, it may or may not be compactly generated. We use this to give a description of K(R-Proj) as a quotient of K(R-Flat). The remarkable fact is that this new description of K(R-Proj) generalizes to non-affine schemes; this will appear in Murfet's thesis.

Original language	English
Pages (from-to)	255-308
Number of pages	54
Journal	Inventiones Mathematicae
Volume	174
Issue number	2
DOIs	https://doi.org/10.1007/s00222-008-0131-0
Publication status	Published - Nov 2008

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abstract = "Let R be a ring. We prove that the homotopy category K(R-Proj) is always א1-compactly generated, and, depending on the ring R, it may or may not be compactly generated. We use this to give a description of K(R-Proj) as a quotient of K(R-Flat). The remarkable fact is that this new description of K(R-Proj) generalizes to non-affine schemes; this will appear in Murfet's thesis.",

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AU - Neeman, Amnon

PY - 2008/11

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N2 - Let R be a ring. We prove that the homotopy category K(R-Proj) is always א1-compactly generated, and, depending on the ring R, it may or may not be compactly generated. We use this to give a description of K(R-Proj) as a quotient of K(R-Flat). The remarkable fact is that this new description of K(R-Proj) generalizes to non-affine schemes; this will appear in Murfet's thesis.

AB - Let R be a ring. We prove that the homotopy category K(R-Proj) is always א1-compactly generated, and, depending on the ring R, it may or may not be compactly generated. We use this to give a description of K(R-Proj) as a quotient of K(R-Flat). The remarkable fact is that this new description of K(R-Proj) generalizes to non-affine schemes; this will appear in Murfet's thesis.

UR - https://www.scopus.com/pages/publications/52549124340

U2 - 10.1007/s00222-008-0131-0

DO - 10.1007/s00222-008-0131-0

M3 - Review article

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VL - 174

SP - 255

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JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

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The homotopy category of flat modules, and Grothendieck duality

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