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

Showing math.ACShow all

14 papers · 1 filter

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.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.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.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.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.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.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}…