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Related papers: Weights and conservativity

200 papers

The purpose of this work is to present a model for 3D massive gravity with topological and higher-derivative terms. Causality and unitarity are discussed at tree-level. Power-counting renormalizability is also contemplated.

General Relativity and Quantum Cosmology · Physics 2015-06-25 Carlos Pinheiro , Gentil O. Pires , Claudio Sasaki

Grafakos systematically proved that $A_\infty$ weights have different characterizations for cubes in Euclidean spaces in his classical text book. Very recently, Duoandikoetxea, Mart\'{\i}n-Reyes, Ombrosi and Kosz discussed several…

Probability · Mathematics 2024-04-23 Jie Ju , Wei Chen , Jingya Cui , Chao Zhang

This article deals with a relationship between derived categories of modules over some partially ordered sets and triangulated categories arising from quasi-homogeneous isolated singularities. It produces heuristics for the existence of…

Combinatorics · Mathematics 2023-10-23 Frédéric Chapoton

This paper introduces a new algebraic notion - triangulated persistence category (TPC) - that refines that of triangulated category in the same sense that a persistence module is a refinement of the notion of a vector space. The spaces of…

Symplectic Geometry · Mathematics 2024-08-13 Paul Biran , Octav Cornea , Jun Zhang

The goal of this paper is to construct a category of motivic "sheaves" on an algebraic variety defined over a subfield of C, using Nori's method. This categoryis abelian and it possesses faithful exact realization functors to the…

Algebraic Geometry · Mathematics 2012-10-11 Donu Arapura

This paper introduces the concept of the dimension of a triangulated category with respect to a fixed full subcategory. For the bounded derived category of an abelian category, upper bounds of the dimension with respect to a contravariantly…

Representation Theory · Mathematics 2013-10-01 Takuma Aihara , Tokuji Araya , Osamu Iyama , Ryo Takahashi , Michio Yoshiwaki

We define exact weights on a triangulated category to be nonnegative functions on objects satisfying a subadditivity condition with respect to exact triangles. Such weights induce a metric on objects in the triangulated category, which we…

Category Theory · Mathematics 2025-02-06 Peter Bubenik , Jose A. Velez-Marulanda

In this paper, we explore when a locally finite triangulated category has dimension zero or finite representation type. We also study generation of derived categories by orthogonal subcategories.

Representation Theory · Mathematics 2018-01-30 Takuma Aihara , Ryo Takahashi

This is a survey on formality results relying on weight structures. A weight structure is a naturally occurring grading on certain differential graded algebras. If this weight satisfies a purity property, one can deduce formality. Algebraic…

Algebraic Topology · Mathematics 2024-06-28 Coline Emprin , Geoffroy Horel

We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences…

Exactly Solvable and Integrable Systems · Physics 2018-05-04 E. V. Ferapontov , M. V. Pavlov , R. F. Vitolo

Using punctual gluing of $t$-structures, we construct an analogue of S. Morel's weight truncation functors (for certain weight profiles) in the setting of motivic sheaves. As an application we construct a canonical motivic analogue of the…

Algebraic Geometry · Mathematics 2018-08-30 Vaibhav Vaish

This thesis embarks on a comprehensive investigation of modified gravity theories and their implications on the properties of compact objects. Our primary objective is to shed light on the fundamental nature of gravity by exploring…

General Relativity and Quantum Cosmology · Physics 2024-06-25 Rajes Ghosh

In earlier work (arXiv:0801.0261), we gave a definition of an abelian category of motivic (constructible) sheaves over a base in characteristic zero using Nori's method. This category has Hodge and etale realizations, and is stable under…

Algebraic Geometry · Mathematics 2022-04-18 Donu Arapura

We introduce the notion of pre-weight structure on a triangulated category and study the corresponding pseudo-identities. We propose the notion of canonical derived equivalence between algebras that are not necessarily flat, which is…

Representation Theory · Mathematics 2025-11-20 Xiao-Wu Chen

This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy…

Classical Physics · Physics 2024-09-13 Jiashi Yang

We study t-structures generated by sets of objects which satisfy a condition weaker than the compactness. We also study weight structures cogenerated by sets of objects satisfying the dual condition. Under some appropriate hypothesis, it…

Category Theory · Mathematics 2020-02-05 George Ciprian Modoi

We prove the well posedness in weighted Sobolev spaces of certain linear and nonlinear elliptic boundary value problems posed on convex domains and under singular forcing. It is assumed that the weights belong to the Muckenhoupt class $A_p$…

Analysis of PDEs · Mathematics 2024-06-18 Tadele Mengesha , Enrique Otarola , Abner J. Salgado

First, we show that a compact object $C$ in a triangulated category, which satisfies suitable conditions, induces a $t$-structure. Second, in an abelian category we show that a complex $P^{\centerdot}$ of small projective objects of term…

Rings and Algebras · Mathematics 2007-05-23 Mitsuo Hoshino , Yoshiaki Kato , Jun-ichi Miyachi

Given a presilting object in a triangulated category, we find necessary and sufficient conditions for the existence of a complement. This is done both for classic (pre)silting objects and for large (pre)silting objects. The key technique is…

Representation Theory · Mathematics 2026-05-25 Lidia Angeleri Hügel , David Pauksztello , Jorge Vitória

This paper explores the restriction behavior of silting-induced $t$-structures and co-$t$-structures on triangulated categories endowed with metrics. For compactly generated triangulated categories admitting small coproducts, silting…

Category Theory · Mathematics 2026-04-30 Wei Hu , Ziheng Liu