English

Arithmetic differential equations on $GL_n$, II: arithmetic Lie theory

Number Theory 2015-01-12 v2

Abstract

Motivated by the search of a concept of linearity in the theory of arithmetic differential equations we introduce here an arithmetic analogue of Lie algebras and a concept of skew arithmetic differential cocycles. We will then construct such skew cocycles, based on certain remarkable lifts of Frobenius for the classical groups GLn,SLn,SOn,SpnGL_n, SL_n, SO_n, Sp_{n}. The theory for GLnGL_n, especially on the Galois side, will be further developed in a sequel to this paper.

Keywords

Cite

@article{arxiv.1308.0744,
  title  = {Arithmetic differential equations on $GL_n$, II: arithmetic Lie theory},
  author = {Alexandru Buium and Taylor Dupuy},
  journal= {arXiv preprint arXiv:1308.0744},
  year   = {2015}
}
R2 v1 2026-06-22T01:03:30.780Z