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Search: MSC category 18E30 ( Derived categories, triangulated categories )

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1. CJM 2014 (vol 67 pp. 28)

Asadollahi, Javad; Hafezi, Rasool; Vahed, Razieh
Bounded Derived Categories of Infinite Quivers: Grothendieck Duality, Reflection Functor
We study bounded derived categories of the category of representations of infinite quivers over a ring $R$. In case $R$ is a commutative noetherian ring with a dualising complex, we investigate an equivalence similar to Grothendieck duality for these categories, while a notion of dualising complex does not apply to them. The quivers we consider are left, resp. right, rooted quivers that are either noetherian or their opposite are noetherian. We also consider reflection functor and generalize a result of Happel to noetherian rings of finite global dimension, instead of fields.

Keywords:derived category, Grothendieck duality, representation of quivers, reflection functor
Categories:18E30, 16G20, 18E40, 16D90, 18A40

2. CJM 2000 (vol 52 pp. 225)

Alonso Tarrío, Leovigildo; Jeremías López, Ana; Souto Salorio, María José
Localization in Categories of Complexes and Unbounded Resolutions
In this paper we show that for a Grothendieck category $\A$ and a complex $E$ in $\CC(\A)$ there is an associated localization endofunctor $\ell$ in $\D(\A)$. This means that $\ell$ is idempotent (in a natural way) and that the objects that go to 0 by $\ell$ are those of the smallest localizing (= triangulated and stable for coproducts) subcategory of $\D(\A)$ that contains $E$. As applications, we construct K-injective resolutions for complexes of objects of $\A$ and derive Brown representability for $\D(\A)$ from the known result for $\D(R\text{-}\mathbf{mod})$, where $R$ is a ring with unit.

Categories:18E30, 18E15, 18E35

3. CJM 1999 (vol 51 pp. 3)

Allday, C.; Puppe, V.
On a Conjecture of Goresky, Kottwitz and MacPherson
We settle a conjecture of Goresky, Kottwitz and MacPherson related to Koszul duality, \ie, to the correspondence between differential graded modules over the exterior algebra and those over the symmetric algebra.

Keywords:Koszul duality, Hirsch-Brown model
Categories:13D25, 18E30, 18G35, 55U15

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