20 citations · 33 across the 17 of their papers we have counts for
22 papers
Arithmetic partial differential operators on ramified extensions of $\ZZ_p$
Marshall Donn, Lance Edward Miller, William D. Taylor
The notion of -derivation as introduced by Buium has a rich history of applications in arithmetic geometry. Working over $\ZZ_p$, Buium-Ralph-Simanca showed that arithmetic diff…
Arithmetic differential geometry in the arithmetic PDE setting II: curvature and cohomology
Alexandru Buium, Lance Edward Miller
This is the second paper in a series devoted to developing an arithmetic PDE analogue of Riemannian geometry. In Part 1 arithmetic PDE analogues of Levi-Civita and Chern connection…
Differentially fixed ideals in toric varieties
Lance Edward Miller, William D. Taylor, Janet Vassilev
This article concerns monomial ideals fixed by differential operators of affine semi-group rings over . We give a complete characterization of when this happens. Perhap…
Arithmetic differential geometry in the arithmetic PDE setting, I: connections
Lance Edward Miller, Alexandru Buium
This is the first in a series on papers developing an arithmetic PDE analogue of Riemannian geometry. The role of partial derivatives is played by Fermat quotient operations with r…
Purely arithmetic PDE's over a p-adic field I: delta-characters and delta-modular forms
Alexandru Buium, Lance Edward Miller
A formalism of arithmetic partial differential equations (PDEs) is being developed in which one considers several arithmetic differentiations at one fixed prime. In this theory sol…
Generalized -depth and graded nilpotent singularities
Kyle Maddox, Lance Edward Miller
We address explicit constructions of new variants of -nilpotent singularities. In particular, we explore how (generalized) weakly -nilpotent singularities behave under gluing…