2,586 research outputs found
Homological algebra with locally compact abelian groups
No full textAbstractIn this article we study locally compact abelian groups using the language of derived categories. We define a derived Hom-functor on the bounded derived category of LCA groups with values in the derived category of Hausdorff topological abelian groups. We introduce a smallness condition for LCA groups and show that the category of such groups has a natural tensor product and internal Hom. Derived versions of these yield closed tensor triangulated categories which may be of arithmetical interest
Periodic twisted cohomology and hBduality
No full textUsing the differentiable structure, twisted 2-periodic de Rham cohomology is well known, and showing up as the target of Chern characters for twisted K-theory. The main motivation of this work is a topological interpretation of two-periodic twisted de Rham cohomology which is generalizable to arbitrary topological spaces and at the same time to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally compact topological stacks with emphasis on: the construction of the sheaf theory operations in unbounded derived categories elements of Verdier duality and integration. The main result is the construction of a functorial periodization associated to a U(1)-gerbe. As an application we verify the T-duality isomorphism in periodic twisted cohomology and in periodic twisted orbispace cohomology
Periodic twisted cohomology and hBduality
No full textUsing the differentiable structure, twisted 2-periodic de Rham cohomology is well known, and showing up as the target of Chern characters for twisted K-theory. The main motivation of this work is a topological interpretation of two-periodic twisted de Rham cohomology which is generalizable to arbitrary topological spaces and at the same time to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally compact topological stacks with emphasis on: the construction of the sheaf theory operations in unbounded derived categories elements of Verdier duality and integration. The main result is the construction of a functorial periodization associated to a U(1)-gerbe. As an application we verify the T-duality isomorphism in periodic twisted cohomology and in periodic twisted orbispace cohomology
Sheaf theory for stacks in manifolds and twisted cohomology for ^1hBHgerbes
No full textIn this paper we give a sheaf theory interpretation of the twisted cohomology of manifolds. To this end we develop a sheaf theory on smooth stacks. The derived push-forward of the constant sheaf with value R along the structure map of a U(1) gerbe over a smooth manifold X is an object of the derived category of sheaves on X. Our main result shows that it is isomorphic in this derived category to a sheaf of twisted de Rham complexes
Algebraic Cobordism and \'Etale Cohomology
Get PDFThomason's \'{e}tale descent theorem for Bott periodic algebraic -theory
\cite{aktec} is generalized to any module over a regular Noetherian
scheme of finite dimension. Over arbitrary Noetherian schemes of finite
dimension, this generalizes the analog of Thomason's theorem for Weibel's
homotopy -theory. This is achieved by amplifying the effects from the case
of motivic cohomology, using the slice spectral sequence in the case of the
universal example of algebraic cobordism. We also obtain integral versions of
these statements: Bousfield localization at \'etale motivic cohomology is the
universal way to impose \'etale descent for these theories. As applications, we
describe the \'etale local objects in modules over these spectra and show that
they satisfy the full six functor formalism, construct an \'etale descent
spectral sequence converging to Bott-inverted motivic Landweber exact theories,
and prove cellularity and effectivity of the \'{e}tale versions of these
motivic spectra.Comment: published version with revised acknowledgements, 70 pages, to appear
in Geometry & Topolog
The first stable homotopy groups of motivic spheres
Get PDFWe compute the 1-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of hermitian and Milnor K-groups. This is achieved by solving questions about convergence and differentials in the slice spectral sequence
Cellularity of hermitian K-theory and Witt-theory
Get PDFHermitian K-theory and Witt-theory are cellular in the sense of stable motivic homotopy
theory over any base scheme without points of characteristic two
Slices of motivic Landweber spectra
Get PDFIn this paper we show that a conjecture of Voevodsky about the slices of the motivic cobordism spectrum implies a statement about the slices of motivic Landweber spectra. Over perfect fields these slices are given by the coefficients of the corresponding topological Landweber spectrum and the motivic Eilenberg MacLane spectrum. We also prove a cohomological version of Landweber exactness which applies to the compact objects of the stable motivic homotopy category
Duality for topological abelian group stacks and ehBduality
No full textWe extend Pontrjagin duality from topological abelian groups to certain locally compact group stacks. To this end we develop a sheaf theory on the big site of topological spaces S in order to prove that the sheaves ExtiShAbS(G,T), i = 1, 2, vanish, where G is the sheaf represented by a locally compact abelian group and T is the circle. As an application of the theory we interpret topological T-duality of principal Tn-bundles in terms of Pontrjagin duality of abelian group stacks
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