Journal of Pure and Applied Algebra最新文献

英文中文

Diagonal tensor algebra and naïve liftings 对角张量代数和天真提升

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-27 DOI: 10.1016/j.jpaa.2024.107808

Saeed Nasseh , Maiko Ono , Yuji Yoshino

The notion of naïve lifting of differential graded (DG) modules along certain DG algebra extensions was introduced by the authors for the purpose of studying problems in homological commutative algebra that involve self-vanishing of Ext. Our goal in this paper is to deeply study naïve lifting property using the diagonal tensor algebra. Our main result provides several characterizations of naïve liftability of DG modules under certain Ext vanishing conditions. As an application, we affirmatively answer a question posed by the authors regarding a specific characterization of naïve liftability.

微分级数（DG）模块沿某些 DG 代数扩展的天真提升概念是作者为了研究同调交换代数中涉及 Ext 自消失的问题而提出的。我们的主要结果提供了 DG 模块在某些 Ext 消失条件下的天真提升性的几个特征。作为应用，我们肯定地回答了作者提出的关于天真可提升性的一个具体特征的问题。

引用次数: 0

The May filtration on THH and faithfully flat descent THH 上的五月过滤和忠实的平缓下降

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-26 DOI: 10.1016/j.jpaa.2024.107806

Liam Keenan

In this article, we study descent properties of topological Hochschild homology and topological cyclic homology. In particular, we verify that both of these invariants satisfy faithfully flat descent and 1-connective descent for connective

E_{2}

-ring spectra. This generalizes a result of Bhatt–Morrow–Scholze from [6] and a result of Dundas–Rognes from [11], respectively. Along the way, we develop some basic theory for cobar constructions and give an alternative presentation of the May filtration on topological Hochschild homology, originally due to Angelini-Knoll–Salch [3].

在本文中，我们研究了拓扑霍赫希尔德同调和拓扑循环同调的下降性质。特别是，我们验证了这两个不变式都满足连通 E2 环谱的忠实平坦下降和 1-connective 下降。这分别推广了[6]中 Bhatt-Morrow-Scholze 的一个结果和[11]中 Dundas-Rognes 的一个结果。在此过程中，我们发展了一些关于科巴构造的基本理论，并给出了拓扑霍赫希尔德同调的梅滤波的另一种表述，该表述最初是由 Angelini-Knoll-Salch [3] 提出的。

引用次数: 0

Examples and cofibrant generation of effective Kan fibrations 有效 Kan 纤维的实例和共纤维生成

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-26 DOI: 10.1016/j.jpaa.2024.107812

Benno van den Berg , Freek Geerligs

We will make two contributions to the theory of effective Kan fibrations, which are a more explicit version of the notion of a Kan fibration, a notion which plays a fundamental role in simplicial homotopy theory. We will show that simplicial Malcev algebras are effective Kan complexes and that the effective Kan fibrations can be seen as the right class in an algebraic weak factorization system. In addition, we will introduce two strengthenings of the notion of an effective Kan fibration, the symmetric effective and degenerate-preferring Kan fibrations, and show that the previous results hold for these strengthenings as well.

我们将对有效阚纤维理论做出两个贡献，有效阚纤维是阚纤维概念的更明确版本，而阚纤维概念在简单同调理论中起着基础性作用。我们将证明简单马尔切夫代数是有效阚复数，而有效阚纤维可视为代数弱因式分解系统中的右类。此外，我们还将介绍有效 Kan 纤维概念的两种强化，即对称有效和变性优选 Kan 纤维，并证明前面的结果也适用于这些强化。

引用次数: 0

Jacobian varieties with group algebra decomposition not affordable by Prym varieties 具有群代数分解的雅各布品种不是普莱姆品种所能负担得起的

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-13 DOI: 10.1016/j.jpaa.2024.107803

Benjamín M. Moraga

The action of a finite group G on a compact Riemann surface X naturally induces another action of G on its Jacobian variety

J (X)

. In many cases, each component of the group algebra decomposition of

J (X)

is isogenous to a Prym varieties of an intermediate covering of the Galois covering

π_{G} : X \to X / G

; in such a case, we say that the group algebra decomposition is affordable by Prym varieties. In this article, we present an infinite family of groups that act on Riemann surfaces in a manner that the group algebra decomposition of

J (X)

is not affordable by Prym varieties; namely, affine groups

Aff (F_{q})

with some exceptions:

q = 2

q = 9

, q a Fermat prime,

q = 2^{n}

with

2^{n} - 1

a Mersenne prime and some particular cases when

X / G

has genus 0 or 1. In each one of this exceptional cases, we give the group algebra decomposition of

J (X)

by Prym varieties.

有限群 G 在紧凑黎曼曲面 X 上的作用自然会引起 G 在其雅各布综 J(X) 上的另一个作用。在许多情况下，J(X) 的群代数分解的每个分量都与伽罗瓦覆盖πG:X→X/G 的中间覆盖的 Prym 变项同源；在这种情况下，我们说群代数分解是由 Prym 变项负担得起的。在这篇文章中，我们提出了一个无穷群族，这些群族作用于黎曼曲面时，J(X) 的群代数分解不能由 Prym varieties 承担；即仿射群 Aff(Fq)，但有一些例外情况：q=2，q=9，q 是费马素数，q=2n，2n-1 是梅森素数，以及 X/G 属 0 或 1 的一些特殊情况。在每一种特殊情况下，我们都给出了 J(X) 的普赖姆变项的群代数分解。

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引用次数: 0

On the transcendental lattices of Hyper-Kähler manifolds 论超凯勒流形的超越网格

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-12 DOI: 10.1016/j.jpaa.2024.107805

Benedetta Piroddi , Ángel David Ríos Ortiz

We introduce the notion of a Hyper-Kähler manifold X induced by a Hodge structure of K3-type. We explore this notion for the known deformation types of Hyper-Kähler manifolds studying those that are induced by a K3 or abelian surface (that is, induced by the Hodge structure of their transcendental lattice), giving lattice-theoretic criteria to decide whether or not they are birational to a moduli space of sheaves over said surface. We highlight the different behaviors we find for the particular class of Hyper-Kähler manifolds of O'Grady type.

我们引入了由 K3 型霍奇结构诱导的超凯勒流形 X 的概念。我们针对已知的超凯勒流形的变形类型探讨了这一概念，研究了那些由 K3 或无性曲面（即由其超越晶格的霍奇结构诱导）诱导的超凯勒流形，给出了晶格理论判定它们是否与所述曲面上的剪切的模空间具有双向性的标准。我们着重强调了在奥格雷迪型超凯勒流形这一特殊类别中发现的不同行为。

引用次数: 0

Some remarks on spin-orbits of unit vectors 关于单位矢量自旋轨道的一些评论

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-10 DOI: 10.1016/j.jpaa.2024.107802

Tariq Syed

For $n \in N$ and a commutative ring R with $2 \in R^{\times}$ , the group $S L_{n} (R)$ acts on the set $U m_{n} (R)$ of unimodular vectors of length n and $S p i n_{2 n} (R)$ acts on the set of unit vectors $U_{2 n - 1} (R)$ . We give an example of a ring for which the comparison map $U m_{n} (R) / S L_{n} (R) \to U_{2 n - 1} (R) / S p i n_{2 n} (R)$ fails to be bijective.

对于 n∈N 和 2∈R× 的交换环 R，群 SLn(R) 作用于长度为 n 的单模向量集 Umn(R)，而 Spin2n(R) 作用于单位向量集 U2n-1(R)。我们举例说明 Umn(R)/SLn(R)→U2n-1(R)/Spin2n(R) 的比较映射不具有双射性的环。

引用次数: 0

On local divisor class groups of complete intersections 论完全相交的局部除数类群

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-10 DOI: 10.1016/j.jpaa.2024.107804

Daniel Windisch

Samuel conjectured in 1961 that a (Noetherian) local complete intersection ring that is a UFD in codimension at most three is itself a UFD. It is said that Grothendieck invented local cohomology to prove this fact. Following the philosophy that a UFD is nothing else than a Krull domain (that is, a normal domain, in the Noetherian case) with trivial divisor class group, we take a closer look at the Samuel–Grothendieck Theorem and prove the following generalization: Let A be a local Cohen–Macaulay ring.

(1)
A is a normal domain if and only if A is a normal domain in codimension at most 1.
(2)
Suppose that A is a normal domain and a complete intersection. Then the divisor class group of A is a subgroup of the projective limit of the divisor class groups of the localizations $A_{p}$ , where p runs through all prime ideals of height at most 3 in A.

We use this fact to describe for an integral Noetherian locally complete intersection scheme X the gap between the groups of Weil and Cartier divisors, generalizing in this case the classical result that these two concepts coincide if X is locally a UFD.

萨缪尔在 1961 年猜想，一个（诺特）局部完全交环在至多三维上是一个 UFD，它本身也是一个 UFD。据说格罗thendieck 发明了局部同调学来证明这一事实。根据 UFD 无非是一个具有微分子类群的 Krull 域（在诺特情况下是一个正域）这一理念，我们仔细研究了塞缪尔-格罗thendieck 定理，并证明了以下概括：(1)当且仅当 A 是标度至多为 1 的正域时，A 是正域。(2)假设 A 是正域和完全交集。我们利用这一事实来描述一个积分诺特局部完全交方案 X 的魏尔组和卡蒂埃分维组之间的差距，并在这种情况下推广经典结果，即如果 X 是局部 UFD，这两个概念是重合的。

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引用次数: 0

Some remarks on relative modular categories 关于相对模块类别的一些评论

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-10 DOI: 10.1016/j.jpaa.2024.107801

Nathan Geer, Bertrand Patureau-Mirand, Matthew Rupert

We study properties of relative modular categories and derive sufficient conditions for their existence. In particular, we derive sufficient conditions for relative pre-modular categories to be non-degenerate and sufficient conditions for the construction of generically semisimple categories.

我们研究相对模块范畴的性质，并推导出它们存在的充分条件。特别是，我们推导了相对前模态范畴非退化的充分条件，以及构造一般半简单范畴的充分条件。

引用次数: 0

Skew power series rings over a prime base ring 素基环上的斜幂级数环

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-10 DOI: 10.1016/j.jpaa.2024.107800

Adam Jones , William Woods

In this paper, we investigate the structure of skew power series rings of the form $S = R [[x; σ, δ]]$ , where R is a complete, positively filtered ring and $(σ, δ)$ is a skew derivation respecting the filtration. Our main focus is on the case in which $σ δ = δ σ$ , and we aim to use techniques in non-commutative valuation theory to address the long-standing open question: if P is an invariant prime ideal of R, is PS a prime ideal of S? When R has characteristic p, our results reduce this to a finite-index problem. We also give preliminary results in the “Iwasawa algebra” case $δ = σ - {id}_{R}$ in arbitrary characteristic. A key step in our argument will be to show that for a large class of Noetherian algebras, the nilradical is “almost” $(σ, δ)$ -invariant in a certain sense.

本文研究了 S=R[[x;σ,δ]] 形式的倾斜幂级数环的结构，其中 R 是完整的正滤波环，(σ,δ) 是尊重滤波的倾斜导数。我们主要关注 σδ=δσ 的情况，旨在利用非交换估价理论中的技术解决一个长期悬而未决的问题：如果 P 是 R 的不变素理想，那么 PS 是 S 的素理想吗？当 R 具有特性 p 时，我们的结果将这一问题简化为有限指数问题。我们还给出了任意特征中δ=σ-idR 的 "岩泽代数 "情形的初步结果。我们论证的关键步骤是证明，对于一大类诺特代数，无根性在一定意义上 "几乎 "是 (σ,δ) 不变的。

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引用次数: 0

Characteristic p approaches to the Jacobian conjecture 雅各布猜想的特征 p 方法

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2024-09-07 DOI: 10.1016/j.jpaa.2024.107797

Jeffrey Lang

We present several versions of the Jacobian Conjecture in characteristic

p > 0

each of which if true would imply the Jacobian Conjecture in characteristic 0. We test these characteristic p versions of the conjecture against several families of Jacobian pairs in characteristic p. Based on the results we propose a characteristic p approach to solving the Jacobian Conjecture in characteristic 0.

我们提出了特征中雅各布猜想的几个版本，每个版本如果成立，都意味着特征 0 中的雅各布猜想。我们用特征中的几组雅各布对检验了猜想的这些特征版本。基于这些结果，我们提出了解决特征 0 中雅各布猜想的特征方法。

引用次数: 0

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