829 research outputs found
Homological Localisation of Model Categories
One of the most useful methods for studying the stable homotopy category is localising at some spectrum E. For an arbitrary stable model category we introduce a candidate
for the Eâlocalisation of this model category. We study the properties of this new construction and relate it to some wellâknown categories
On the derived category of a regular toric scheme
Let X be a quasi-compact scheme, equipped with an open covering by affine
schemes. A quasi-coherent sheaf on X gives rise, by taking sections over the
covering sets, to a diagram of modules over the various coordinate rings. The
resulting "twisted" diagram of modules satisfies a certain gluing condition,
stating that the data is compatible with restriction to smaller open sets.
In case X is a regular toric scheme over an arbitrary commutative ring, we
prove that the unbounded derived category D(X) of quasi-coherent sheaves on X
can be obtained from a category of twisted diagrams which do not necessarily
satisfy any gluing condition by inverting maps which induce homology
isomorphisms on hyper-derived inverse limits. Moreover, we given an explicit
construction of a finite set of weak generators for the derived category.
For example, if X is projective n-space then D(X) is generated by n+1
successive twists of the structure sheaf; the present paper gives a new
homotopy-theoretic proof of this classical result.
The approach taken uses the language of model categories, and the machinery
of Bousfield-Hirschhorn colocalisation. The first step is to characterise
colocal objects; these turn out to be homotopy sheaves in the sense that chain
complexes over different open sets agree on intersections up to
quasi-isomorphism only. In a second step it is shown that the homotopy category
of homotopy sheaves is the derived category of X.Comment: 35 pages; diagrams need post script viewer or PDF v2: removed
"completeness" assumption, changed titl
Vanishing lines in generalized Adams spectral sequences are generic
We show that in a generalized Adams spectral sequence, the presence of a
vanishing line of fixed slope (at some term of the spectral sequence, with some
intercept) is a generic property.Comment: 11 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol3/paper7.abs.htm
Operations on integral lifts of K(n)
This very rough sketch is a sequel to arXiv:1808.08587; it presents evidence
that operations on lifts of the functors K(n) to cohomology theories with
values in modules over valuation rings of local number fields, indexed by
Lubin-Tate groups of such fields, are extensions of the groups of automorphisms
of the indexing group laws, by the exterior algebras on the normal bundle to
the orbits of the group laws in the space of lifts.Comment: \S 2.0 hopefully less cryptic. To appear in the proceedings of the
2015 Nagoya conference honoring T Ohkawa. Comments very welcome
MiR-888: A newly identified miRNA significantly over-expressed in endometrial cancers
Endometrial cancer is the most common gynecological malignancy and the fourth most common cancer in women. With accumulating evidence, microRNAs have emerged as significant players in the development and progression of cancers. The data points to miR-888 playing an important functional role in the development of aggressive endometrial tumors. Future research will focus on identifying and validating the targets of miR-888 to elucidate its mechanism of action and support this hypothesi
Morita base change in Hopf-cyclic (co)homology
In this paper, we establish the invariance of cyclic (co)homology of left
Hopf algebroids under the change of Morita equivalent base algebras. The
classical result on Morita invariance for cyclic homology of associative
algebras appears as a special example of this theory. In our main application
we consider the Morita equivalence between the algebra of complex-valued smooth
functions on the classical 2-torus and the coordinate algebra of the
noncommutative 2-torus with rational parameter. We then construct a Morita base
change left Hopf algebroid over this noncommutative 2-torus and show that its
cyclic (co)homology can be computed by means of the homology of the Lie
algebroid of vector fields on the classical 2-torus.Comment: Final version to appear in Lett. Math. Phy
Excision for simplicial sheaves on the Stein site and Gromov's Oka principle
A complex manifold satisfies the Oka-Grauert property if the inclusion
\Cal O(S,X) \hookrightarrow \Cal C(S,X) is a weak equivalence for every Stein
manifold , where the spaces of holomorphic and continuous maps from to
are given the compact-open topology. Gromov's Oka principle states that if
has a spray, then it has the Oka-Grauert property. The purpose of this
paper is to investigate the Oka-Grauert property using homotopical algebra. We
embed the category of complex manifolds into the model category of simplicial
sheaves on the site of Stein manifolds. Our main result is that the Oka-Grauert
property is equivalent to representing a finite homotopy sheaf on the Stein
site. This expresses the Oka-Grauert property in purely holomorphic terms,
without reference to continuous maps.Comment: Version 3 contains a few very minor improvement
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