Related papers: Strict units of commutative ring spectra
Previous research on exceptional units has primarily focused on the ring of rational integers or abstract finite rings, often restricted to linear or quadratic constraints. In this paper, we extend the concept of polynomial-type exceptional…
We develop a theory of R-module Thom spectra for a commutative symmetric ring spectrum R and we analyze their multiplicative properties. As an interesting source of examples, we show that R-algebra Thom spectra associated to the special…
We view strict ring spectra as generalized rings. The study of their algebraic K-theory is motivated by its applications to the automorphism groups of compact manifolds. Partial calculations of algebraic K-theory for the sphere spectrum are…
We find explicit formulae for the circular spectral measures of $E_7,E_8$. This leads to a number of general observations regarding the ADE circular measures: these are linear combinations of measures supported by the roots of unity, with…
This paper studies the integral cohomology ring of the classifying space $BPU_n$ of the projective unitary group $PU_n$. By calculating a Serre spectral sequence, we determine the ring stucture of $H^*(BPU_n;\mathbb{Z})$ in dimensions $\leq…
We give a formula for the geometric fixed-points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to…
In this paper we compute the sum of the $k$-th powers over any finite commutative unital rings, thus generalizing known results for finite fields, the rings of integers modulo $n$ or the ring of Gaussian integers modulo $n$. As an…
In an earlier paper, we defined and studied q-analogues of the Stirling numbers of both types for the Coxeter group of type B. In the present work, we show how this approach can be extended to all irreducible complex reflection groups G.…
Spectral approximation by polynomials on the unit ball is studied in the frame of the Sobolev spaces $W^{s}_p(\ball)$, $1<p<\infty$. The main results give sharp estimates on the order of approximation by polynomials in the Sobolev spaces…
In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…
In this paper we study the category of discrete G-spectra for a profinite group G. We consider an embedding of module objects in spectra into a category of module objects in discrete G-spectra, and study the relationship between the…
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact…
We give a functorial construction of k-invariants for ring spectra and use these to classify extensions in the Postnikov tower of a ring spectrum.
In this paper, we study the computational complexity of the commutative determinant polynomial computed by a class of set-multilinear circuits which we call regular set-multilinear circuits. Regular set-multilinear circuits are commutative…
Tensoring finite pointed simplicial sets with commutative ring spectra yields important homology theories such as (higher) topological Hochschild homology and torus homology. We prove several structural properties of these constructions…
Let $G$ be a finite group of order $n$, and $\xi$ an $n$-th primitive root of unity. Consider the affine scheme $C:=\mbox{Spc}({\mathbb Z}[\xi]\otimes_{\mathbb Z} R(G))$ where $R(G)$ is the representation ring of $G$. We study the fibers of…
We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric groups and of extensions in the category of strict polynomial…
Two trace formulas for the spectra of arbitrary Hermitian matrices are derived by transforming the given Hermitian matrix $H$ to a unitary analogue. In the first type the unitary matrix is $e^{i(\lambda\II - H)}$ where $\lambda$ is the…
In [F. Xu, On the cohomology rings of small categories, J. Pure Appl. Algebra 212 (2008), 2555-2569], Xu constructs a LHS-spectral sequence for target regular extensions of small categories. We extend this construction to ext-groups and…
We determine the Gross-Hopkins duals of certain higher real $K$-theory spectra. More specifically, let $p$ be an odd prime, and consider the Morava $E$-theory spectrum of height $n=p-1$. It is known, in the expert circles, that for certain…