Related papers: A new basis for the complex $K$-theory cooperation…

In this article, we give an explicit construction of the $p$-adic Fourier transform by Schneider and Teitelbaum, which allows for the investigation of the integral property. As an application, we give a certain integral basis of the space…

We use the multiplicative structure of the Koszul resolution to give short and simple proofs of some known estimates for the total dimension of the cohomology of spaces which admit free torus actions and analogous results for filtered…

We give a formula comparing the E-series of the moduli stacks of rank 2 degree 0 semistable Higgs bundles in genus $g \geq 2$ to intersection E-polynomials of its coarse moduli space. A parellel formula holds in various 2-Calabi-Yau…

Consider a system of polynomials in many variables over the ring of integers of a number field $K$. We prove an asymptotic formula for the number of integral zeros of this system in homogeneously expanding boxes. As a consequence, any…

For an affine algebraic variety, we introduce algebraic Gelfand-Fuks cohomology of polynomial vector fields with coefficients in differentiable $AV$-modules. Its complex is given by cochains that are differential operators in the sense of…

Let $K$ be a field of characteristic zero. Let $R = K[X_0, X_1,\ldots,X_n]$ be standard graded. Let $A_{n+1}(K)$ be the $(n + 1)^{th}$ Weyl algebra over $K$. Let $I$ be a homogeneous ideal of $R$ and let $M = H^i_I(R)$ for some $i \geq 0$.…

Let A be a separable unital nuclear purely infinite simple C*-algebra satisfying the Universal Coefficient Theorem, and such that the K_0-class of the identity is zero. We prove that every automorphism of order two of the K-theory of A is…

The paper is an inquiry of the algebraic foundations of the theory of dispersionless integrable hierarchies, like the dispersionless KP and modified KP hierarchies and the universal Whitham's hierarchy of genus zero. It stands out for the…

In prior joint work with Lewis, we developed a theory of enriched set-valued $P$-partitions to construct a $K$-theoretic generalization of the Hopf algebra of peak quasisymmetric functions. Here, we situate this object in a diagram of six…

We compute the generic degrees of the Ariki--Koike algebras by first constructing a basis of matrix units in the semisimple case. As a consequence, we also obtain an explicit isomorphism from any semisimple Ariki--Koike algebra to the group…

We propose a new definition of Koszulity for graded algebras where the degree zero part has finite global dimension, but is not necessarily semi-simple. The standard Koszul duality theorems hold in this setting. We give an application to…

We first summarize the basic structure of the outer distribution module of a completely regular code. Then, employing a simple lemma concerning eigenvectors in association schemes, we propose to study the tightest case, where the indices of…

We provide a new foundation for combinatorial commutative algebra and Stanley-Reisner theory using the partition complex introduced in [Adi18]. One of the main advantages is that it is entirely self-contained, using only a minimal knowledge…

We compute the ring of cooperations $\pi_{**}^{\mathbb{F}_q}(\text{kq} \otimes \text{kq})$ for the very effective Hermitian K-theory over all finite fields $\mathbb{F}_q$ where $\text{char}(\mathbb{F}_q) \neq 2.$ To do this, we use the…

Kempf [1976] studied proper, G-equivariant maps from equivariant vector bundles over flag manifolds to G-representations V, which he called _collapsings_. We give a simple formula for the G-equivariant cohomology class on V,…

We derive some consequences of the Liouville theorem for plurisubharmonic functions of L.-F. Tam and the author. The first result provides a nonlinear version of the complex splitting theorem (which splits off a factor of $\mathbb{C}$…

A general notion of detection is introduced and used in the study of the cohomology of elementary abelian 2-groups with respect to the spectra in the Postnikov tower of orthogonal K-theory. This recovers and extends results of Bruner and…

We show that the Brauer algebra over the complex numbers for an integral parameter delta can be equipped with a grading, in the case of delta being non-zero turning it into a graded quasi-hereditary algebra. In which case it is Morita…

We consider $A$-hypergeometric (or GKZ-)systems in the case where the grading (character) group is an arbitrary finitely generated Abelian group. Emulating the approach taken for classical GKZ-systems in arXiv:math/0406383 that allows for a…

For primes $p\geq 5 $, $K(KU_p)$ -- the algebraic $K$-theory spectrum of $(KU)^{\wedge}_p$, Morava $K$-theory $K(1)$, and Smith-Toda complex $V(1)$, Ausoni and Rognes conjectured (alongside related conjectures) that $L_{K(1)}S^0…