Vanishing of cohomology over Cohen–Macaulay rings

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Vanishing of cohomology over Cohen–Macaulay rings. / Christensen, Lars Winther; Holm, Henrik Granau.

I: Manuscripta Mathematica, Bind 139, Nr. 3-4, 2012, s. 535-544.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Christensen, LW & Holm, HG 2012, 'Vanishing of cohomology over Cohen–Macaulay rings', Manuscripta Mathematica, bind 139, nr. 3-4, s. 535-544. https://doi.org/10.1007/s00229-012-0540-7

APA

Christensen, L. W., & Holm, H. G. (2012). Vanishing of cohomology over Cohen–Macaulay rings. Manuscripta Mathematica, 139(3-4), 535-544. https://doi.org/10.1007/s00229-012-0540-7

Vancouver

Christensen LW, Holm HG. Vanishing of cohomology over Cohen–Macaulay rings. Manuscripta Mathematica. 2012;139(3-4):535-544. https://doi.org/10.1007/s00229-012-0540-7

Author

Christensen, Lars Winther ; Holm, Henrik Granau. / Vanishing of cohomology over Cohen–Macaulay rings. I: Manuscripta Mathematica. 2012 ; Bind 139, Nr. 3-4. s. 535-544.

Bibtex

@article{3c77e19f80ca46d4be4b71e8d126a6a1,
title = "Vanishing of cohomology over Cohen–Macaulay rings",
abstract = "A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings—colloquially called AC rings—that satisfy a natural condition on vanishing of cohomology. Several results attest to the remarkable homological properties of AC rings, but their definition is barely operational, and it remains unknown if they form a class that is closed under typical constructions in ring theory. In this paper, we study transfer of the AC property along local homomorphisms of Cohen–Macaulay rings. In particular, we show that the AC property is preserved by standard procedures in local algebra. Our results also yield new examples of Cohen–Macaulay AC rings.",
author = "Christensen, {Lars Winther} and Holm, {Henrik Granau}",
year = "2012",
doi = "10.1007/s00229-012-0540-7",
language = "English",
volume = "139",
pages = "535--544",
journal = "Manuscripta Mathematica",
issn = "0025-2611",
publisher = "Springer",
number = "3-4",

}

RIS

TY - JOUR

T1 - Vanishing of cohomology over Cohen–Macaulay rings

AU - Christensen, Lars Winther

AU - Holm, Henrik Granau

PY - 2012

Y1 - 2012

N2 - A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings—colloquially called AC rings—that satisfy a natural condition on vanishing of cohomology. Several results attest to the remarkable homological properties of AC rings, but their definition is barely operational, and it remains unknown if they form a class that is closed under typical constructions in ring theory. In this paper, we study transfer of the AC property along local homomorphisms of Cohen–Macaulay rings. In particular, we show that the AC property is preserved by standard procedures in local algebra. Our results also yield new examples of Cohen–Macaulay AC rings.

AB - A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings—colloquially called AC rings—that satisfy a natural condition on vanishing of cohomology. Several results attest to the remarkable homological properties of AC rings, but their definition is barely operational, and it remains unknown if they form a class that is closed under typical constructions in ring theory. In this paper, we study transfer of the AC property along local homomorphisms of Cohen–Macaulay rings. In particular, we show that the AC property is preserved by standard procedures in local algebra. Our results also yield new examples of Cohen–Macaulay AC rings.

U2 - 10.1007/s00229-012-0540-7

DO - 10.1007/s00229-012-0540-7

M3 - Journal article

VL - 139

SP - 535

EP - 544

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 3-4

ER -

ID: 41928345