47 research outputs found
Periodizable motivic ring spectra
We show that the cellular objects in the module category over a motivic E
infinity ring spectrum E can be described as the module category over a graded
topological spectrum if E is strongly periodizable in our language. A similar
statement is proven for triangulated categories of motives. Since MGL is
strongly periodizable we obtain topological incarnations of motivic Landweber
spectra. Under some categorical assumptions the unit object of the model
category for triangulated motives is as well strongly periodizable giving
motivic cochains whose module category models integral triangulated categories
of Tate motives.Comment: 15 page
Relations between slices and quotients of the algebraic cobordism spectrum
We prove a relative statement about the slices of the algebraic cobordism
spectrum. If the map from MGL to a certain quotient of MGL introduced by
Hopkins and Morel is the map to the zero-slice then a relative version of
Voevodsky's conjecture on the slices of MGL holds true. We outline the picture
for K-theory and rational slices.Comment: 15 pages; misprints correcte
Homological algebra with locally compact abelian groups
In this article we study locally compact abelian (LCA) groups from the
viewpoint of derived categories, using that their category is quasi-abelian in
the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex
with values in the derived category of Hausdorff topological abelian groups.
Furthermore we introduce a smallness condition for LCA groups and show that
such groups have a natural tensor product and internal Hom which both admit
derived versions.Comment: 18 pages, AMSLaTe
Inertia and delocalized twisted cohomology
We show that the inertia stack of a topological stack is again a topological
stack. We further observe that the inertia stack of an orbispace is again an
orbispace. We show how a U(1)-banded gerbe over an orbispace gives rise to a
flat line bundle over its inertia stack. Via sheaf theory over topological
stacks it gives rise to the twisted delocalized cohomology of the orbispace.
With these results and constructions we generalize concepts, which are
well-known in the smooth framework, to the topological case. In the smooth case
we show, that our sheaf-theoretic definition of twisted delocalized cohomology
of orbispaces coincides with former definitions using a twisted de Rham
complex.Comment: 42 page
Periodic twisted cohomology and T-duality
The initial motivation of this work was to give a topological interpretation
of two-periodic twisted de-Rham cohomology which is generalizable 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 functor associated to a U(1)-gerbe. As applications we verify the
-duality isomorphism in periodic twisted cohomology and in periodic twisted
orbispace cohomology.Comment: 128 pages; v2: small corrections (e.g. of typos), version to appear
in Asterisqu