James Gillespie

activity

20062023

most citedThe stable module category of a general ring

85 citations · 124 across the 19 of their papers we have counts for

collaborators

28 papers

math.AG2023

K-flatness in Grothendieck categories: Application to quasi-coherent sheaves

Sergio Estrada, James Gillespie, Sinem Odabaşı

Let $(G, \otimes)$ be any closed symmetric monoidal Grothendieck category. We show that K-flat covers exist universally in the category of chain complexes and that the Ver…

math.AT2022

The homotopy category of acyclic complexes of pure-projective modules

James Gillespie

Let $R$ be any ring with identity. We show that the homotopy category of all acyclic chain complexes of pure-projective $R$ -modules is a compactly generated triangulated category.…

math.AC2021

Ding injective envelopes in the category of complexes

James Gillespie, Alina Iacob

A complex $X$ is called Ding injective if there exists an exact sequence of injective complexes $\dots \to E_{1} \to E_{0} \to E_{- 1} \to \dots$ such…

math.AT2021

K-flat complexes and derived categories

James Gillespie

Let $R$ be a ring with identity. Inspired by recent work of Emmanouil, we show that the derived category of $R$ is equivalent to the chain homotopy category of all K-flat complexes…

math.KT2021

Duality pairs, generalized Gorenstein modules, and Ding injective envelopes

James Gillespie, Alina Iacob

Let $R$ be a general ring. Duality pairs of $R$ -modules were introduced by Holm-Jorgensen. Most examples satisfy further properties making them what we call semi-complete duality p…

math.AT2021

Quillen equivalences inducing Grothendieck duality for unbounded chain complexes of sheaves

Sergio Estrada, James Gillespie

Let $X$ be a semiseparated Noetherian scheme with a dualizing complex $D$ . We lift some well-known triangulated equivalences associated with Grothendieck duality to Quille…