5 papers
-depth and -nilpotent rings: generalizations and applications
Kyle Maddox, Lance Edward Miller
Computation of the Frobenius closure of ideals in rings of prime characteristic is a difficult problem. For a given ideal, its Frobenius test exponent provides a valuable degree of…
Derived jet and arc spaces
Roi Docampo, Lance Edward Miller, C. Eric Overton-Walker
We study jet schemes and arc spaces in the context of derived algebraic geometry. Explicitly, we consider the jet and arc functors in the category of schemes and study their animat…
A Buchsbaum theory for Frobenius closure
Kriti Goel, Kyle Maddox, Lance Edward Miller +2
We give a partial characterization for when the difference is independent of the choice of parameter ideal in a…
Higher dimensional geometry of -jets
Lance Edward Miller, Jackson S. Morrow
In this work, we prove a quantitative version of the prime-to- Manin--Mumford conjecture for varieties with ample cotangent bundle. More precisely, let be an abelian variety…
Rees algebras and generalized depth-like conditions in prime characteristic
Alessandra Costantini, Kyle Maddox, Lance Edward Miller
In this article we address a question concerning nilpotent Frobenius actions on Rees algebras and associated graded rings. We prove a nilpotent analog of a theorem of Huneke for Co…