3 papers
math.AC2026
Derived complete intersections and polynomial growth of Betti numbers over dg-algebras
Michael K. Brown, Justin Lyle
A theorem of Gulliksen states that a local ring is a complete intersection if and only if the Betti numbers of its finitely generated modules grow polynomially. We prove a derived…
math.AC2026
The derived depth formula for modules of finite quasi-projective dimension
Luigi Ferraro, Justin Lyle
Let be a commutative Noetherian local ring. We prove a variety of new formulae for modules of finite quasi-projective or finite quasi-injective dimension. These include the Der…
math.AC2026
G-levels of perfect complexes
Lars Winther Christensen, Antonia Kekkou, Justin Lyle +2
We prove that a commutative noetherian ring is Gorenstein of dimension at most if is an upper bound on the G-levels of perfect -complexes. For local, we prove…