Bounded Derived Categories of Infinite Quivers: Grothendieck Duality, Reflection Functor

Asadollahi, Javad ; Hafezi, Rasool ; Vahed, Razieh

Canadian journal of mathematics, Tome 67 (2015) no. 1, pp. 28-54

Résumé

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.

Détail

DOI : 10.4153/CJM-2014-018-7

Mots-clés : 18E30, 16G20, 18E40, 16D90, 18A40, Derived Category, Grothendieck duality, representation of quivers, reflection functor

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