Related papers: Higher Order Dualities between Prime Ideals
We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSI's. The recently introduced duality on SSI's is given an effective conceptual and computational setting. We study strongly…
We unconditionally improve the uniformity in the Chebotarev density theorem for Galois extensions of number fields using nonabelian base change. This leads to the first theoretical improvement over Weiss's bound for the least norm of an…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
We survey research that studies the connection between the computational complexity of optimization problems on the one hand, and the duality gap between the primal and dual optimization problems on the other. To our knowledge, this is the…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
This article focuses on approximately prime rings and approximately prime ideals in proximal relator spaces, especially in descriptive proximity spaces. In particular, we define some binary operations, including the product of two…
In this paper, we present a new method to derive formulas for the generating functions of interval orders, counted with respect to their size, magnitude, and number of minimal and maximal elements. Our method allows us not only to…
In this paper we present several finite families of congruences between cusp forms and Eisenstein series of higher weights at powers of prime ideals. We formulate a conjecture which describes properties of the prime ideals and their…
In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose…
We study various cases of dualities between $\cal{N}$$=1$ 5d supersymmetric gauge theories. We motivate the dualities using brane webs, and provide evidence for them by comparing the superconformal index. In many cases we find that the…
The aim of this paper is to study jumping numbers and multiplier ideals of any ideal in a two-dimensional local ring with a rational singularity. In particular we reveal which information encoded in a multiplier ideal determines the next…
A mixed type dual to a nondifferentiable variational problem involving higher order derivative is formulated and duality results are proved under generalized invexity conditions. Special cases are generated from our results.
We use higher ideles and duality theorems to develop a universal approach to higher dimensional class field theory.
In this work, we use the recently introduced double-dilation construction by Zwart and Coecke to construct a new categorical probabilistic theory of density hypercubes. By considering multi-slit experiments, we show that the theory displays…
We show how one can ascertain the values of a complete set of mutually complementary observables of a prime degree of freedom.
Recently a powerful duality between color and kinematics has been proposed for integrands of scattering amplitudes in quite general gauge theories. In this paper the duality proposal is extended to the more general class of gauge theory…
Using elementary means, we prove several identities involving the M\"obius function, generalizing in the multidimensional case well-known formulas coming from convolution arguments.
In this paper, we analyze properties of prime number sequences produced by the alternating sum of higher-order subsequences of the primes. We also introduce a new sieve which will generate these prime number sequences via the systematic…
We introduce and study a notion of duality for two classes of optimization problems commonly occurring in probability theory. That is, on an abstract measurable space $(\Omega,\mathcal{F})$, we consider pairs $(E,\mathcal{G})$ where $E$ is…
Closure operations such as tight and integral closure and test ideals have appeared frequently in the study of commutative algebra. This articles serves as a survey of the authors' prior results connecting closure operations, test ideals,…