## 8 Citations

### Arithmetic differential geometry in the arithmetic PDE setting, I: connections

- Mathematics
- 2022

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 respect to several…

### Semi-galois categories II: An arithmetic analogue of Christol's theorem

- MathematicsJournal of Algebra
- 2018

### Arithmetic Analogues of Hamiltonian Systems

- MathematicsIntegrable Systems and Algebraic Geometry
- 2020

The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.

### Lie invariant Frobenius lifts on linear algebraic groups

- Mathematics
- 2018

We show that if $G$ is a linear algebraic group over a number field and if $G$ is not a torus then for all but finitely many primes $p$ the $p$-adic completion of $G$ does not possess a Frobenius…

### Purely arithmetic PDE's over a p-adic field I: delta-characters and delta-modular forms

- Mathematics
- 2021

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 solutions can be…

### Curvature in noncommutative geometry

- MathematicsAdvances in Noncommutative Geometry
- 2019

Our understanding of the notion of curvature in a noncommutative setting has progressed substantially in the past 10 years. This new episode in noncommutative geometry started when a Gauss-Bonnet…

### Arithmetic Levi–Cività connection

- MathematicsSelecta Mathematica
- 2019

This paper is part of a series of papers where an arithmetic analogue of classical differential geometry is being developed. In this arithmetic differential geometry functions are replaced by integer…

### Invariant Frobenius lifts and deformation of the Hasse invariant

- Mathematics
- 2018

We show that the $p$-adic completion of any affine elliptic curve with ordinary reduction possesses Frobenius lifts whose "normalized" action on $1$-forms preserves mod $p$ the space of invariant…

## References

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THIS volume is the first to be produced of the projected nine volumes of the collected papers of the late Prof. H. A. Lorentz. It contains a number of papersnineteen in all, mainly printed…

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- Mosc. Math. J
- 2004

### Schemes over F1 and zeta functions

- Compositio Mathematica, 146 (6),
- 2010

### Arithmetic Differential Equations

- Mathematics
- 2005

Main concepts and results: Preliminaries from algebraic geometry Outline of $\delta$-geometry General theory: Global theory Local theory Birational theory Applications: Spherical correspondences Flat…

### Arithmetic differential equations on $GL_n$, III: Galois groups

- Mathematics
- 2013

Differential equations have arithmetic analogues in which derivatives are replaced by Fermat quotients; these analogues are called arithmetic differential equations and the present paper is concerned…

### Le Groupe Fondamental de la Droite Projective Moins Trois Points

- 1989

Le present article doit beaucoup a A. Grothendieck. Il a invente la philosophie des motifs, qui est notre fil directeur. Il y a quelques cinq ans, il m’a aussi dit, avec force, que le complete…