Arithmetic differential equations on GLₙ, II: arithmetic Lie theory

الأصل · EN

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, Spₙ. The theory for GLₙ, especially on the Galois side, will be further developed in a sequel to this paper.