It is a well established fact that the notions of quasi-abelian categories\nand tilting torsion pairs are equivalent. This equivalence fits in a wider\npicture including tilting pairs of $t$-structures.\nFirstly, we extend this picture into a hierarchy of $n$-quasi-abelian\ncategories and $...
We give a definition of quasi-coherent modules for any presheaf of sets on the categories of affine commutative and non-commutative schemes. This definition generalizes the usual one. We study the property of a quasi-coherent module to be a sheaf in various topologies. Using presheaves of group...
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By looking at the moduli stack of regular G-Higgs bundles, we prove that it induces a banded gerbe structure on a slightly larger stack, whose band is given by sheaves of tori. This characterization yields a cocyclic description of the fibres of the corresponding Hitchin map by means of ...
Symmetric monoidal categoriesNon-noetherian schemesLet X be a scheme over an abelian symmetric monoidal category (C, circle times, 1) satisfying certain conditions. In this article, we develop the theory of the derived category D(O-x - QCoh) of quasi-coherent sheaves on X (where X is not...
Finally we show that the points of a Noetherian, quasi-compact and semi-separated scheme $X$ over such a field object $K$ in $(\\mathcal C,\\otimes,1)$ can be recovered from certain kinds of functors between categories of quasi-coherent sheaves. The latter is a partial generalization ...
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. This class is stable under algebraic deformation, giving rise to a 1-1 correspondence between ...
Non-commutative deformations and quasi-coherent modules We identify a class of "quasi-compact semi-separated" (qcss) twisted presheaves of algebras A for which well-behaved Grothendieck abelian categories of qua... H Dinh Van,L Liu,W Lowen - 《Selecta Mathematica》 被引量: 5发表: 2017年 Th...