# A general construction of Weil functors

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1 Analyse IECL - Institut Élie Cartan de Lorraine 2 IECL - Institut Élie Cartan de Lorraine

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 = KX-X^{k+1}\$. We investigate some algebraic aspects of these general Weil functors -K-theory of Weil functors-, action of the -Galois group- \$\Aut KA\$, which will be of importance for subsequent applications to general differential geometry.

Keywords : Taylor expansion differential calculus jet scalar extension Weil functor

Autor: Wolfgang Bertram - Arnaud Souvay -

Fuente: https://hal.archives-ouvertes.fr/

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