Acyclicity versus total acyclicity for complexes over noetherian rings
Srikanth Iyengar, Henning Krause
Abstract
It is proved that for a commutative noetherian ring with dualizing complex the homotopy category of projective modules is equivalent, as a triangulated category, to the homotopy category of injective modules. Restricted to compact objects, this statement is a reinterpretation of Grothendieck's duality theorem. Using this equivalence it is proved that the (Verdier) quotient of the category of acyclic complexes of projectives by its subcategory of totally acyclic complexes and the corresponding category consisting of injective modules are equivalent. A new characterization is provided for complexes in Auslander categories and in Bass categories of such rings.
Create a lesson
Related papers
On the weak Lefschetz property of Artinian Gorenstein algebras of codimension three in arbitrary characteristic
Omkar Javadekar
Linear Independence of Polynomial Compositions and Identifiability of Deep Neural Networks
Kathlén Kohn, Giovanni Luca Marchetti, Alex Massarenti et al.
Comparing v-numbers of symbolic and ordinary powers of squarefree monomial ideals
Trung Chau, Tài Huy Hà, A. V. Jayanthan et al.
Polynomial extensions do not preserve the strong finite type property
Viet-Hoang Tran, Phan Thanh Toan, Thieu N. Vo et al.
Reduction numbers for witnesses to the generalized Loewy length
Richard Bartels, Sarah Dajani, Gabriel Koomson
Multi-graded generic initial ideals, regularity, and the optimal colorful fractional Helly theorem for d-Leray complexes
Daniel McGinnis