Related papers: Detecting and describing ramification for structur…
For an additive Waldhausen category linear over a ring $k$, the corresponding $K$-theory spectrum is a module spectrum over the $K$-theory spectrum of $k$. Thus if $k$ is a finite field of characteristic $p$, then after localization at $p$,…
We investigate Tate cohomology of modules over a commutative noetherian ring with respect to semidualizing modules. We identify classes of modules admitting Tate resolutions and analyze the interaction between the corresponding relative and…
We study functors underlying derived Hochschild cohomology, also called Shukla cohomology, of a commutative algebra S essentially of finite type and of finite flat dimension over a commutative noetherian ring K. We construct a complex of…
Let $f:C\rightarrow D$ be a nonconstant separable morphism between irreducible smooth projective curves defined over an algebraically closed field. We say that $f$ is genuinely ramified if ${\mathcal O}_D$ is the maximal semistable…
We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order…
We set up a homological algebra for N-complexes, which are graded modules together with a degree -1 endomorphism d satisfying d^N=0. We define Tor- and Ext-groups for N-complexes and we compute them in terms of their classical counterparts…
A quadratic form over a Henselian-valued field of arbitrary residue characteristic is tame if it becomes hyperbolic over a tamely ramified extension. The Witt group of tame quadratic forms is shown to be canonically isomorphic to the Witt…
We give a homotopy invariant construction of the Reidemeister trace for the coincidence of two maps between closed manifolds of not necessarily the same dimensions. It is realized as a homology class of the homotopy equalizer, which…
Let $K$ be a complete discrete valuation field with residue class field $k$, where both are of positive characteristic $p$. Then the group of wild automorphisms of $K$ can be identified with the group under composition of formal power…
We categorify the inclusion-exclusion principle for partially ordered topological spaces and schemes to a filtration on the derived category of sheaves. As a consequence, we obtain functorial spectral sequences that generalize the two…
Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…
Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diagonalization exists. Existing approaches provide only partial…
The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild…
The wild de Rham spaces parameterize isomorphism classes of (stable) meromorphic connections, defined on principal bundles over wild Riemann surfaces. Working on the Riemann sphere, we will deformation-quantize the standard open part of de…
If A is a homotopy cartesian square of ring spectra satisfying connectivity hypotheses, then the cube induced by Goodwillie's integral cyclotomic trace from K(A) to TC(A) is homotopy cartesian. In other words, the homotopy fiber of the…
Tate-Hochschild cohomology of an algebra is a generalization of ordinary Hochschild cohomology, which is defined on positive and negative degrees and has a ring structure. Our purpose of this paper is to study the eventual periodicity of an…
In this paper we investigate how germs of real functions can change under deformation. In particular we look at deformations of germs of isolated singularities from R_n to R_k (n >= k) and the relation with there natural stratification in…
In recent years, Benson, Iyengar and Krause have developed a theory of stratification for compactly generated triangulated categories with an action of a graded commutative Noetherian ring. Stratification implies a classification of…
We conjecture that a $p$-algebra over a complete discrete valued field $K$ contains a totally ramified purely inseparable subfield if and only if it contains a totally ramified cyclic maximal subfield. We prove the conjecture in several…
Modern categories of spectra such as that of Elmendorf et al equipped with strictly symmetric monoidal smash products allows the introduction of symmetric monoids providing a new way to study highly coherent commutative ring spectra. These…