Related papers: On higher Du Bois singularities and $K$-regularity

For $K$ an infinite field of characteristic other than two, consider the action of the special orthogonal group $\operatorname{SO}_t(K)$ on a polynomial ring via copies of the regular representation. When $K$ has characteristic zero,…

We develop differential algebraic K-theory of regular arithmetic schemes. Our approach is based on a new construction of a functorial, spectrum level Beilinson regulator using differential forms. We construct a cycle map which represents…

In this paper, we define an invariant, which we believe should be the substitute for total K-theory in the case when there is one distinguished ideal. Moreover, some diagrams relating the new groups to the ordinary K-groups with…

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

We determine the structure of the weak*-closed $G$-invariant ideals in the Fourier-Stieltjes algebra $B(G)$ of certain groups $G$ by means of a $K$-theoretical obstruction. The groups to which this applies are groups whose only irreducible…

The paper revisits concretely the algebraic K-theory in the light of the global program of Langlands by taking into account the new algebraic interpretation of homotopy viewed as deformation(s) of Galois representations given by…

Bounds on the Castelnuovo-Mumford regularity of the associated graded modules of k-Buchsbaum modules M are given in terms of k and some other invariants of M.

In this note we apply Guillen-Navarro descent theorem, \cite{GN02}, to define a descent variant of the algebraic $K$-theory of varieties over a field of characteristic zero, $\mathcal{KD}(X)$, which coincides with $\mathcal{K}(X)$ for…

Let $X$ be a complex algebraic variety. With $\mathbb{Q}$-coefficients, the compactly supported cohomology groups $H^{i}_{c}(X, \mathbb{Q})$ and the compactly supported intersection cohomology groups $IH^{i}_{c}(X, \mathbb{Q})$ have mixed…

Using twisted nearby cycles, we define a new notion of slopes for complex holonomic D-modules. We prove a boundedness result for these slopes, study their functoriality and use them to characterize regularity. For a family of (possibly…

In this paper we introduce a new formalism for $K$-theory, called squares $K$-theory. This formalism allows us to simultaneously generalize the usual three-term relation $[B] = [A] + [C]$ for an exact sequence $A \hookrightarrow B…

A generalization of the Davenport constant is investigated. For a finite abelian group $G$ and a positive integer $k$, let $D_k(G)$ denote the smallest $\ell$ such that each sequence over $G$ of length at least $\ell$ has $k$ disjoint…

We introduce and study invariants of singularities in positive characteristic called F-thresholds. They give an analogue of the jumping coefficients of multiplier ideals in characteristic zero. We discuss the connection between the…

Non-trivial K-theory groups and non-trivial cobordism groups can lead to global symmetries which are conjectured to be absent in quantum gravity. Inspired by open-closed string duality, we propose a correspondence between the two groups,…

Inspired by methods in prime characteristic in commutative algebra, we introduce and study combinatorial invariants of seminormal monoids. We relate such numbers with the singularities and homological invariants of the semigroup ring…

Let $G$ be a finite subgroup of $\text{SL}(2,\Bbbk)$ and let $R = \Bbbk[x,y]^G$ be the coordinate ring of the corresponding Kleinian singularity. In 1998, Crawley-Boevey and Holland defined deformations $\mathcal{O}^\lambda$ of $R$…

We explore a relationship between the classical representation theory of a complex, semisimple Lie algebra \g and the resonance varieties R(V,K)\subset V^* attached to irreducible \g-modules V and submodules K\subset V\wedge V. In the…

Spectral morphisms between Banach algebras are useful for comparing their K-theory and their "noncommutative dimensions" as expressed by various notions of stable ranks. In practice, one often encounters situations where the spectral…

We study notions of hyperuniformity for invariant locally square-integrable point processes in regular trees. We show that such point processes are never geometrically hyperuniform, and if the diffraction measure has support in the…

Suppose $G$ is a finite group and $A\subseteq G$ is such that $\{gA:g\in G\}$ has VC-dimension strictly less than $k$. We find algebraically well-structured sets in $G$ which, up to a chosen $\epsilon>0$, describe the structure of $A$ and…