Markus Spitzweck

Motivic slices and coloured operads

Colored operads were introduced in the 1970s for the purpose of studying homotopy invariant algebraic structures on topological spaces. In this paper we introduce colored operads in motivic stable homotopy theory. Our main motivation is to uncover hitherto unknown highly structured properties of the slice filtration. The latter decomposes every motivic spectrum into its slices, which are motives, and one may ask to what extend the slice filtration preserves highly structured objects such as algebras and modules. We use colored operads to give a precise solution to this problem. Our approach makes use of axiomatic setups which specialize to classical and motivic stable homotopy theory. Accessible t-structures are central to the development of the general theory. Concise introductions to colored operads and Bousfield (co)localizations are given in separate appendices.

Duality for topological abelian group stacks and T-duality

We investigate when Isomorphism Conjectures, such as the ones due to Baum-Connes, Bost and Farrell-Jones, are stable under colimits of groups over directed sets (with not necessarily injective structure maps). We show in particular that both the K-theoretic Farrell-Jones Conjecture and the Bost Conjecture with coefficients hold for those groups for which Higson, Lafforgue and Skandalis have disproved the Baum-Connes Conjecture with coefficients.We present a

Sheaf theory for stacks in manifolds and twisted cohomology for S 1 -gerbes

C^*

Homological algebra with locally compact abelian groups

-algebra which is naturally associated to the

Inertia and delocalized twisted cohomology

ax+b

Motivic approach to limit sheaves

-semigroup over

Operads, Algebras and Modules in General Model Categories

\mathbb N

Motivic Landweber Exactness

. It is simple and purely infinite and can be obtained from the algebra considered by Bost and Connes by adding one unitary generator which corresponds to addition. Its stabilization can be described as a crossed product of the algebra of continuous functions, vanishing at infinity, on the space of finite adeles for

A commutative P1-spectrum representing motivic cohomology over Dedekind domains

\mathbb Q

Relations between slices and quotients of the algebraic cobordism spectrum

by the natural action of the