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 ...
For every morphism of schemes f:Y→X we have a pullback functor ⁎f⁎:Qcoh(X)→Qcoh(Y) between categories of quasi-coherent sheaves. It preserves direct sums, cokernels and tensor products, i.e. it is a cocontinuous symmetric monoidal functor. In this paper, we are concerned with...
Left coherence implies that the category of finitely presented left modules over the ring is abelian. This category might then be considered as being analogous to the category of coherent sheaves on an affine commutative variety. Thus, coherence is the initial point for developing noncommutative ...
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 ...
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 ...