Results 1 to 10 of about 11,745 (80)
Local and stable homological algebra in Grothendieck abelian categories [PDF]
Homology, Homotopy and Applications, 2007 We define model category structures on the category of chain complexes over a Grothendieck abelian category depending on the choice of a generating family, and we study their behaviour with respect to tensor products and stabilization. This gives convenient tools to construct and understand triangulated categories of motives and we consider here the ...
Cisinski, Denis-Charles +1 more
openaire +5 more sources
Grothendieck groups of categories of abelian varieties [PDF]
European Journal of Mathematics, 2017 We compute the Grothendieck group of the category of abelian varieties over an algebraically closed field $k$. We also compute the Grothendieck group of the category of $A$-isotypic abelian varieties, for any simple abelian variety $A$, assuming $k$ has characteristic 0, and for any elliptic curve $A$ in any characteristic.
openaire +3 more sources
Auslander-Reiten duality for Grothendieck abelian categories [PDF]
Transactions of the American Mathematical Society, 2018 Auslander-Reiten duality for module categories is generalised to Grothendieck abelian categories that have a sufficient supply of finitely presented objects. It is shown that Auslander-Reiten duality amounts to the fact that the functor Ext^1(C,-) into modules over the endomorphism ring of C admits a partially defined right adjoint when C is a finitely
openaire +2 more sources
Completions of Grothendieck groups [PDF]
, 2011 For a certain class of abelian categories, we show how to make sense of the "Euler characteristic" of an infinite projective resolution (or, more generally, certain chain complexes that are only bounded above), by passing to a suitable completion of the ...
Achar, Pramod N., Stroppel, Catharina
core +3 more sources
Specialization orders on atom spectra of Grothendieck categories [PDF]
, 2015 We introduce systematic methods to construct Grothendieck categories from colored quivers and develop a theory of the specialization orders on the atom spectra of Grothendieck categories.
Kanda, Ryo
core +1 more source
Derived equivalences induced by big cotilting modules [PDF]
, 2014 We prove that given a Grothendieck category G with a tilting object of finite projective dimension, the induced triangle equivalence sends an injective cogenerator of G to a big cotilting module.
Stovicek, Jan
core +1 more source
Non-commutative deformations and quasi-coherent modules [PDF]
, 2015 We identify a class of "quasi-compact semi-separated" (qcss) twisted presheaves of algebras A for which well-behaved Grothendieck abelian categories of quasi-coherent modules Qch(A) are defined.
Liu, Liyu, Lowen, Wendy, Van, Hoang Dinh
core +1 more source
Thomason cohomology of categories [PDF]
, 2012 We introduce cohomology and homology theories for small categories with general coefficient systems from simplex categories first studied by Thomason.
Andrew Tonks +34 more
core +5 more sources
Grothendieck categories as a bilocalization of linear sites
, 2017 We prove that the 2-category Grt of Grothendieck abelian categories with colimit preserving functors and natural transformations is a bicategory of fractions in the sense of Pronk of the 2-category Site of linear sites with continuous morphisms of sites ...
González, Julia Ramos
core +1 more source
On the tensor product of linear sites and Grothendieck categories
, 2017 We define a tensor product of linear sites, and a resulting tensor product of Grothendieck categories based upon their representations as categories of linear sheaves.
González, Julia Ramos +2 more
core +1 more source