The notes connect Lie derivatives to differential equations on algebraic D-varieties and present an account of Ax's theorem as an entry point for students.
Buium, Differential algebraic groups of finite dimension, Springer 1992
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Notes on Lie derivatives, algebraic D-varieties, and Ax's theorem
The notes connect Lie derivatives to differential equations on algebraic D-varieties and present an account of Ax's theorem as an entry point for students.