𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Gorenstein categories and Tate cohomology on projective schemes

✍ Scribed by E. Enochs; S. Estrada; J. R. García–Rozas

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
222 KB
Volume
281
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We study Gorenstein categories. We show that such a category has Tate cohomological functors and Avramov–Martsinkovsky exact sequences connecting the Gorenstein relative, the absolute and the Tate cohomological functors. We show that such a category has what Hovey calls an injective model structure and also a projective model structure in case the category has enough projectives. As examples we show that if X is a locally Gorenstein projective scheme then the category 𝔔𝔠𝔬(X) of quasi‐coherent sheaves on X is such a category and so has these features. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Relative singularity categories and Gore
Relative singularity categories and Gorenstein-projective modules
✍ Xiao-Wu Chen 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 178 KB

## Abstract We introduce the notion of relative singularity category with respect to a self‐orthogonal subcategory ω of an abelian category. We introduce the Frobenius category of ω‐Cohen‐Macaulay objects, and under certain conditions, we show that the stable category of ω‐Cohen‐Macaulay objects is