Related papers: Modules homotopiques (Homotopy modules)

The positive cohomology groups of a finite group acting on a ring vanish when the ring has a norm-one element. In this note we give explicit homotopies on the level of cochains when the group is cyclic, which allows us to express any…

In this article, we construct a Hecke-equivariant Chow motive whose realizations equal intersection cohomology of Siegel threefolds with regular algebraic coefficients. As a consequence, we are able to define Grothendieck motives for Siegel…

We show that the bounded derived category of regular holonomic D-modules on a smooth variety is equivalent to the homotopy catgory of compact (or constructible) modules over the motivic ring spectrum $H_{dR}$ representing algebraic de Rham…

The main result of this paper is the proof for elliptic modular threefolds of conjectures on the existence and structure of a filtration on the Chow groups of smooth projective varieties. In the form we prove them these conjectures were…

In this note we study the functoriality of the coniveau filtration in motivic homotopy theory via a moving lemma over a base scheme, extending previous works of Levine and Bachmann-Yakerson. The main result is that the motivic stable…

Multiplicative Hitchin systems are analogues of Hitchin's integrable system based on moduli spaces of G-Higgs bundles on a curve C where the Higgs field is group-valued, rather than Lie algebra valued. We discuss the relationship between…

We describe the behaviour of the homotopy similarity relations and finite-order invariants under the function $[X,Y]\to[X,Z]$ induced by a map $Y\to Z$ strongly $r$-similar to the constant map.

This paper introduces a new cohomology theory for schemes of finite type over an arithmetic ring. The main motivation for this Arakelov-theoretic version of motivic cohomology is the conjecture on special values of $L$-functions and zeta…

We give an explicit characterization for group extensions that correspond to elements of the symmetric cohomology $HS^2(G,A)$. We also give conditions for the map $HS^n(G,A)\to H^n(G,A)$ to be injective.

A cocycle category H(X,Y) is defined for objects X and Y in a model category, and it is shown that the set of morphisms [X,Y] is isomorphic to the set of path components of H(X,Y) provided the ambient model category is right proper and…

The de Rham stack construction of Simpson shows that D-modules are quasicoherent sheaves on a modified geometry. Drinfeld furthermore introduced the ring stack perspective (aka transmutation), which asserts that a coefficient theory is…

We prove that groups that are mod-p-homology equivalent are isomorphic modulo any term of their derived p-series, in precise analogy to Stallings' 1963 result for the lower-central p-series. Similarly spaces that are mod-p-homology…

We show that, over a local complete intersection, every possible variety is realized as the cohomological support variety of some module. Moreover, we show that the projective variety of a complete indecomposable maximal Cohen-Macaulay…

We consider the set of H\"older continuous cocycles over a finite shift acting on a group of Lipschitz homeomorphisms Lip(G), where G is a metrisable compact topological group. We establish that two dominated cocycles that coincide over…

Let X --> B be an orientable sphere bundle. Its Gysin sequence exhibits H^*(X) as an extension of H^*(B)-modules. We prove that the class of this extension is the image of a canonical class that we define in the Hochschild 3-cohomology of…

We define a trace map for every cohomological correspondence in the motivic stable homotopy category over a general base scheme, which takes values in the twisted bivariant groups. Local contributions to the trace map give rise to quadratic…

We extend the homotopy theories based on point reduction for finite spaces and simplicial complexes to finite acyclic categories and $\Delta$-complexes, respectively. The functors of classifying spaces and face posets are compatible with…

A fundamental observation of Iwasawa gives a criterion for a module over the classical Iwasawa algebra to be torsion. In this paper, we study a certain extension of this criterion. We will then apply this to study the structure of the…

We prove a conjecture of Morel identifying Voevodsky's homotopy invariant sheaves with transfers with spectra in the stable homotopy category which are concentrated in degree zero for the homotopy t-structure and have a trivial action of…

We prove two theorems on cohomologically complete complexes. These theorems are inspired by, and yield an alternative proof of, a recent theorem of P. Schenzel on complete modules.