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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





Author: Wolfgang Bertram - Arnaud Souvay -

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



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