A general construction of Weil functors

Wolfgang Bertram (1) , Arnaud Souvay (1)

1 IECL - Institut Élie Cartan de Lorraine

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.

Mots clés: Taylor expansion; differential calculus; jet; Weil functor; scalar extension

Domaines: Géométrie différentielle [math.DG]

Wolfgang Bertram, Arnaud Souvay. A general construction of Weil functors. Cahiers de topologie et géométrie différentielle catégoriques, 2014, 55 (4), pp.267-313. ⟨hal-00639958v2⟩