Peder Thompson

activity

20152026

most citedMinimal complexes of cotorsion flat modules

10 citations · 35 across the 17 of their papers we have counts for

collaborators

23 papers

math.AC2026

Cosyzygy modules

Petter Andreas Bergh, David A. Jorgensen, Peder Thompson

We characterize all first cosyzygy modules of a given finitely generated module over a local ring. We do this by introducing the notion of a canonical cosyzygy module, and showing…

math.RA2025

Acyclic complexes and regular rings

Lars Winther Christensen, Sergio Estrada, Peder Thompson

A 2009 paper by Iacob and Iyengar characterizes noetherian regular rings in terms of properties of complexes of projective modules, flat modules, and injective modules. We show tha…

math.RA2023

One-sided Gorenstein rings

Lars Winther Christensen, Sergio Estrada, Li Liang +2

Distinctive characteristics of Iwanaga--Gorenstein rings are typically understood through their intrinsic symmetry. We show that several of those that pertain to the Gorenstein glo…

math.AC2023

Dimension and depth inequalities over complete intersections

Petter Andreas Bergh, David A. Jorgensen, Peder Thompson

For a pair of finitely generated modules $M$ and $N$ over a codimension $c$ complete intersection ring $R$ with $ℓ (M \otimes_{R} N)$ finite, we pay special attention to the inequali…

math.RA2022★ 2 cited

Five theorems on Gorenstein global dimensions

Lars Winther Christensen, Sergio Estrada, Peder Thompson

We expand on two existing characterizations of rings of Gorenstein (weak) global dimension zero and give two new characterizations of rings of finite Gorenstein (weak) global dimen…

math.AC2022

The trace property in preenveloping classes

Haydee Lindo, Peder Thompson

We develop the theory of trace modules up to isomorphism and explore the relationship between preenveloping classes of modules and the property of being a trace module, guided by t…

math.AC2021

Rigidity of Ext and Tor via flat-cotorsion theory

Lars Winther Christensen, Luigi Ferraro, Peder Thompson

Let p be a prime ideal in a commutative noetherian ring R and denote by k(p) the residue field of the local ring R_p. We prove that if an R-module M satisfies Ext_R^n(k(p),M) = 0 f…

math.RA2021

Gorenstein weak global dimension is symmetric

Lars Winther Christensen, Sergio Estrada, Peder Thompson

We study the Gorenstein weak global dimension of associative rings and its relation to the Gorenstein global dimension. In particular, we prove the conjecture that the Gorenstein w…

math.AC2020

Asymptotic behavior of Ext for pairs of modules of large complexity over graded complete intersections

David A. Jorgensen, Liana M. Şega, Peder Thompson

Let $M$ and $N$ be finitely generated graded modules over a graded complete intersection $R$ such that $Ext_{R}^{i} (M, N)$ has finite length for all $i ≫ 0$ . We show tha…

math.KT2020

The singularity category of an exact category applied to characterize Gorenstein schemes

Lars Winther Christensen, Nanqing Ding, Sergio Estrada +3

We study singularity categories of exact categories with a focus on those associated to a complete hereditary cotorsion pair. As an application we identify a non-affine analogue of…

math.RA2019★ 2 cited

A refinement of Gorenstein flat dimension via the flat--cotorsion theory

Lars Winther Christensen, Sergio Estrada, Li Liang +3

We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring--the Gorenstein flat-cotorsion dimension--and prove that it, unlike the Gorenstein…

math.AC2019

Reducibility of parameter ideals in low powers of the maximal ideal

Katharine Shultis, Peder Thompson

A commutative noetherian local ring $(R, m)$ is Gorenstein if and only if every parameter ideal of $R$ is irreducible. Although irreducible parameter ideals may exist in…

math.AC2019★ 3 cited

Minimal semi-flat-cotorsion replacements and cosupport

Tsutomu Nakamura, Peder Thompson

Over a commutative noetherian ring $R$ of finite Krull dimension, we show that every complex of flat cotorsion $R$ -modules decomposes as a direct sum of a minimal complex and a con…

math.AC2019

Matrix factorizations for self-orthogonal categories of modules

Petter Andreas Bergh, Peder Thompson

For a commutative ring $S$ and self-orthogonal subcategory $C$ of $Mod (S)$ , we consider matrix factorizations whose modules belong to $C$ . Let $f \in S$ b…

math.AC2019

The stable category of Gorenstein flat sheaves on a noetherian scheme

Lars Winther Christensen, Sergio Estrada, Peder Thompson

For a semi-separated noetherian scheme, we show that the category of cotorsion Gorenstein flat quasi-coherent sheaves is Frobenius and a natural non-affine analogue of the category…

math.RA2018

Homotopy categories of totally acyclic complexes with applications to the flat-cotorsion theory

Lars Winther Christensen, Sergio Estrada, Peder Thompson

We introduce a notion of total acyclicity associated to a subcategory of an abelian category and consider the Gorenstein objects they define. These Gorenstein objects form a Froben…

math.AC2018

Pure-minimal chain complexes

Lars Winther Christensen, Peder Thompson

We introduce a notion of pure-minimality for chain complexes of modules and show that it coincides with (homotopic) minimality in standard settings, while being a more useful notio…

math.AC2017★ 5 cited

Cosupport computations for finitely generated modules over commutative noetherian rings

Peder Thompson

We show that the cosupport of a commutative noetherian ring is precisely the set of primes appearing in a minimal pure-injective resolution of the ring. As an application of this,…

math.AC2017★ 10 cited

Minimal complexes of cotorsion flat modules

Peder Thompson

Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-modules to be minimal, in the sense that every self homotopy equivalence is an isomorphis…

math.AC2016

Detecting Koszulness and related homological properties from the algebra structure of Koszul homology

Amanda Croll, Roger Dellaca, Anjan Gupta +6

Let $k$ be a field and $R$ a standard graded $k$ -algebra. We denote by $H^{R}$ the homology algebra of the Koszul complex on a minimal set of generators of the irrelev…

math.KT2016★ 5 cited

Adams Operations on Matrix Factorizations

Michael K. Brown, Claudia Miller, Peder Thompson +1

We define Adams operations on matrix factorizations, and we show these operations enjoy analogues of several key properties of the Adams operations on perfect complexes with suppor…

math.KT2016★ 7 cited

Cyclic Adams Operations

Michael K. Brown, Claudia Miller, Peder Thompson +1

Let $Q$ be a commutative, Noetherian ring and $Z \subseteq Spec (Q)$ a closed subset. Define $K_{0}^{Z} (Q)$ to be the Grothendieck group of those bounded complexes of fin…

math.AC2015★ 1 cited

Stable Local Cohomology

Peder Thompson

Let $R$ be a Gorenstein local ring, $a$ an ideal in $R$ , and $M$ an $R$ -module. The local cohomology of $M$ supported at $a$ can be computed by applying the $\frak{a}…