Results 1 to 10 of about 317,331 (198)
On the derived functors of the third symmetric-power functor [PDF]
arXiv, 2009 We compute the derived functors of the third symmetric-power functor and their cross-effects for certain values. These calculations match predictions by the first named author and largely prove them in general.
Koeck, Bernhard, Satkurunath, Ramesh
arxiv +6 more sources
Cohomology as the derived functor of derivations [PDF]
Transactions of the American Mathematical Society, 1966 Introduction. The investigations which produced this paper were suggested by the fact that the Hochschild cohomology H(F, M) of a free algebra E, with coefficients in any module M, is zero in dimension ^ 2. Since free algebras are projectives in the category of algebras, this suggested that H(—,M), considered as a functor of the first variable, ought ...
Michael Barr, George S. Rinehart
openalex +2 more sources
Gorenstein derived functors [PDF]
Proceedings of the American Mathematical Society, 2004 Over any associative ring R R it is standard to derive H o m R ( − , − ) \mathrm {Hom}_R(-,-) using projective resolutions in the first variable, or injective resolutions in the second variable, and doing this ...
Henrik Holm
openalex +4 more sources
Abstract local cohomology functors [PDF]
arXiv, 2010 We propose to define the notion of abstract local cohomology functors. The derived functors of the ordinary local cohomology functor with support in the closed subset defined by an ideal and the generalized local cohomology functor associated with a given pair of ideals are characterized as elements of the set of all the abstract local cohomology ...
Yoshino, Yuji, Yoshizawa, Takeshi
arxiv +5 more sources
Derivation functors and Lusztig's induction functors [PDF]
arXiv, 2022 Lusztig proved the compatibility of induction functors and restriction functors for Lusztig's perverse sheaves. Fang-Lan-Xiao established a categorification of Green's formula and gave a sheaf-level proof of this compatibility for all semisimple complexes.
arxiv +3 more sources
Derived category of weak chain U-complexes [PDF]
HeliyonIn this paper, we define the derived category of weak chain U-complexes, and we give a characterization of any weak chain U-complex as an object in the right bounded homotopy category of weak chain U-complexes of projective modules.
Fajar Yuliawan +3 more
doaj +2 more sources
Derived equivalences of functor categories [PDF]
Journal of Pure and Applied Algebra, 2019 Let $\Mod \CS$ denote the category of $\CS$-modules, where $\CS$ is a small category. Using the notion of relative derived categories of functor categories, we generalize Rickard's theorem on derived equivalences of module categories over rings to $\Mod \
Asadollahi, J., Hafezi, R., Vahed, R.
core +5 more sources
Derived Functors Related to Wall Crossing [PDF]
arXiv, 2008 The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this transformation is a left exact functor.
Kevin J. Carlin
arxiv +3 more sources
Derived functors of nonadditive functors and homotopy theory [PDF]
Algebraic & Geometric Topology, 2011 The text has been corrected and augmented.
Lawrence Breen, Roman Mikhailov
openalex +6 more sources
A note on deriving unbounded functors of exact categories, with applications to Ind- and Pro- functors [PDF]
arXiv, 2021 In this short note we show that under very mild conditions on a functor between exact categories $F:\mathcal{D}\rightarrow\mathcal{E}$ it is possible to derive $F$ at the level of unbounded complexes. We also give applications to deriving functors between $Pro$- and $Ind$- categories.
Jack Kelly
arxiv +3 more sources