A general construction of Weil functors

Abstract

We construct the Weil functor $T^A$ corresponding to a general Weil algebra $A=K\oplus N$: this is a functor from the category of manifolds over a general topological base field or ring $K$ (of arbitrary characteristic) to the category of manifolds over $A$. This result simultaneously generalizes results known for ordinary, real manifolds, and previous results by the first author for the case of the higher order tangent functors ($A=T^{k}K$) and for the case of jet rings ($A=K[X]/(X^{k+1})$). We investigate some algebraic aspects of these general Weil functors ("K-theory of Weil functors", action of the "Galois group" $\Aut_K(A)$), which will be of importance for subsequent applications to general differential geometry.

V2: minor corrections and improvements

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