Related papers: The algebraic chromatic splitting conjecture for N…

Hindman conjectured that any finite partition of $\mathbb{N}$ has a monochromatic $\{x,y,x+y,xy\}$. Recently, Bowen proved the result for all 2-partition. In this paper, we extend Bowen's result to any semiring $(S,+,\cdot)$ such that $Ss$…

We consider a large class of monomial maps respecting an action of the infinite symmetric group, and prove that the toric ideals arising as their kernels are finitely generated up to symmetry. Our class includes many important examples…

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? This note provides, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov…

The coprimary filtration is a basic construction in commutative algebra. In this article, we prove the existence and uniqueness of coprimary filtration of modules (not necessarily finitely generated) over a Noetherian ring. Moreover, we…

We show that the splitting conjecture in the hybrid model of Gonek--Hughes--Keating holds to order on the Riemann hypothesis. Our results are valid in a larger range of the parameter $X$ which mediates between the partial Euler and Hadamard…

We calculate the homotopy type of $L_1L_{K(2)}S^0$ and $L_{K(1)}L_{K(2)}S^0$ at the prime 2, where $L_{K(n)}$ is localization with respect to Morava $K$-theory and $L_1$ localization with respect to $2$-local $K$ theory. In $L_1L_{K(2)}S^0$…

We describe chromatic localisations of genuine L-spectra of discrete rings and deduce that the purity property of $K(1)$-local $K$-theory of rings established by Bhatt-Clausen-Mathew also holds in Grothendieck-Witt theory. In addition, we…

Let R be a commutative ring with unity (not necessarily finite). The ring R consider as a simple graph whose vertices are the elements of R with two distinct vertices x and y are adjacent if xy=0 in R, where 0 is the zero element of R. In…

In the present paper, we define a notion of numerical equivalence on Chow groups or Grothendieck groups of Noetherian local rings, which is an analogue of that on smooth projective varieties. Under a mild condition, it is proved that the…

For finite-dimensional algebras over a field, Koenig and Yang established a bijection between silting complexes and simple-minded collections in the bounded derived category, with further contributions by many authors in various settings.…

Exceptional points (EPs), singularities in non-Hermitian systems where eigenvalues and eigenstates coalesce, exhibit a dramatically enhanced response to perturbations compared to Hermitian degeneracies. This makes them exceptional…

Let $k$ be a noetherian commutative ring and let $G$ be a finite flat group scheme over $k$. Let $G$ act rationally on a finitely generated commutative $k$-algebra $A$. We show that the cohomology algebra $H^*(G,A)$ is a finitely generated…

Let $R$ be a {\em differentiably simple Noetherian commutative} ring of characteristic $p>0$ (then $(R, \gm)$ is local with $n:= {\rm emdim} (R)<\infty$). A short proof is given of the Theorem of Harper \cite{Harper61} on classification of…

We show that every quasi-compact and quasi-separated algebraic stack can be approximated by a noetherian algebraic stack. We give several applications such as eliminating noetherian hypotheses in the theory of good moduli spaces.

We prove that the infinite half-spin representations are topologically Noetherian with respect to the infinite spin group. As a consequence we obtain that half-spin varieties, which we introduce, are defined by the pullback of equations at…

Let $S^{\cdot}$ be a noetherian graded algebra over a commutative $k$-algebra $A$, where $k$ is a commutative ring, and assume it is a module over a Lie algebroid ${\mathfrak g}_{A/k}$. If $S^\cdot$ is semi-simple over ${\mathfrak g}_{A/k}$…

We show that for a Noetherian ring $A$ that is $I$-adically complete for an ideal $I$, if $A/I$ admits a dualizing complex, so does $A$. This gives an alternative proof of the fact that a Noetherian complete local ring admits a dualizing…

We prove a Noether's theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and…

Let kq denote the very effective cover of the motivic Hermitian K-theory spectrum. We analyze the ring of cooperations $\pi^\mathbb{R}_{**}(\text{kq} \otimes \text{kq})$ in the stable motivic homotopy category $\text{SH}(\mathbb{R})$,…

Inspired by the Ax--Kochen isomorphism theorem, we develop a notion of categorical ultraproducts to capture the generic behavior of an infinite collection of mathematical objects. We employ this theory to give an asymptotic solution to the…