3 papers
math.AC2026
-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…
math.AC2023
Counting geometric branches via the Frobenius map and -nilpotent singularities
Hailong Dao, Kyle Maddox, Vaibhav Pandey
We give an explicit formula to count the number of geometric branches of a curve in positive characteristic using the theory of tight closure. This formula readily shows that the p…
math.AC2022
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…