Geodesic
Derived categories of absolutely flat rings
Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 45-64.

Voir la notice de l'article provenant de la source International Press of Boston

Let $S$ be a commutative ring with topologically noetherian spectrum, and let $R$ be the absolutely flat approximation of $S$. We prove that subsets of the spectrum of $R$ parametrise the localising subcategories of $\mathsf{D}(R)$. Moreover, we prove the telescope conjecture holds for $\mathsf{D}(R)$. We also consider unbounded derived categories of absolutely flat rings that are not semi-artinian and exhibit a localising subcategory that is not a Bousfield class and a cohomological Bousfield class that is not a Bousfield class.
DOI : 10.4310/HHA.2014.v16.n2.a3
Classification : 16E50, 18E30
Keywords: derived category, absolutely flat ring, localising subcategory, telescope conjecture 
@article{HHA_2014_16_2_a2,
     author = {Greg Stevenson},
     title = {Derived categories of absolutely flat rings},
     journal = {Homology, homotopy, and applications},
     pages = {45--64},
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     number = {2},
     year = {2014},
     doi = {10.4310/HHA.2014.v16.n2.a3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n2.a3/}
}
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Greg Stevenson. Derived categories of absolutely flat rings. Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 45-64. doi : 10.4310/HHA.2014.v16.n2.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n2.a3/

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