10 citations · 44 across the 30 of their papers we have counts for
36 papers
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…
The -invariant theory of Hecke correspondences on
Alexandru Buium, Adrian Vasiu
Let be a prime, let be an integer prime to , let be the ring of -typical Witt vectors with coefficients in an algebraic closure of , and consid…
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…
Perfectoid spaces arising from arithmetic jet spaces
Alexandru Buium, Lance Edward Miller
Using arithmetic jet spaces, we attach perfectoid spaces to smooth schemes and to -morphisms of smooth schemes. We also study perfectoid spaces attached to arithmetic differenti…
Solutions to arithmetic differential equations in algebraically closed fields
Alexandru Buium, Lance Edward Miller
We prove that the main examples in the theory of algebraic differential equations possess a remarkable total differential overconvergence property. This allows one to consider solu…