Showing papers on "Ringed space published in 2016"
TL;DR: In this paper, the authors define Z2n-supermanifolds and provide examples in the ringed space and coordinate settings, and show that formal series are the appropriate substitute for nilpotency.
Abstract: In physics and in mathematics Z2n-gradings, n ≥ 2, appear in various fields. The corresponding sign rule is determined by the “scalar product” of the involved Z2n-degrees. The Z2n-supergeometry exhibits challenging differences with the classical one: nonzero degree even coordinates are not nilpotent, and even (respectively, odd) coordinates do not necessarily commute (respectively, anticommute) pairwise. In this article we develop the foundations of the theory: we define Z2n-supermanifolds and provide examples in the ringed space and coordinate settings. We thus show that formal series are the appropriate substitute for nilpotency. Moreover, the class of Z2•-supermanifolds is closed with respect to the tangent and cotangent functors. We explain that any n-fold vector bundle has a canonical “superization” to a Z2n-supermanifold and prove that the fundamental theorem describing supermorphisms in terms of coordinates can be extended to the Z2n-context.
46 citations
16 Mar 2016
TL;DR: In this paper, the dg-category of twisted complexes on a ringed space was studied and a new dgenhancement of the derived category of perfect complexes on that space was proposed.
Abstract: We study the dg-category of twisted complexes on a ringed space and prove that it gives a new dg-enhancement of the derived category of perfect complexes on that space. A twisted complex is a collection of locally defined sheaves together with the homotopic gluing data. We construct a dg-functor from twisted complexes to perfect complexes, which turns out to be a dg-enhancement. This new enhancement has the advantage of being completely geometric and it comes directly from the definition of perfect complex. In addition we will talk about some applications and further topics around twisted complexes.
7 citations
01 Jan 2016
TL;DR: In this paper, Grothendieck's six functors formalism for derived categories of sheaves on ringed spaces over a field was lifted to differential graded enhancements and two applications concerning homological smoothness of derived categories were given.
Abstract: We lift Grothendieck’s six functor formalism for derived categories of sheaves on ringed spaces over a field to differential graded enhancements. Two applications concerning homological smoothness of derived categories of schemes are given.
5 citations
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TL;DR: In this article, the dg-category of twisted perfect complexes on a ringed space with soft structure sheaf was studied, and it was shown that this dg category is quasi-equivalent to that of complex of vector bundles on that space.
Abstract: In this paper we study the dg-category of twisted perfect complexes on a ringed space with soft structure sheaf We prove that this dg-category is quasi-equivalent to the dg-category of complexes of vector bundles on that space This result could be considered as a dg-enhancement of the classic result on soft sheaves in SGA6
2 citations