Weil函子的一般构造
A general construction of Weil functors
摘要：
我们构造了对应于一般Weil代数$A = K \oplus N$的Weil函子$T^A$：这是从一般拓扑基域或环$K$（具有任意特征）上的流形范畴到$A$上的流形范畴的函子.这一结果同时推广了已知的结果为普通，真正的流形，和以前的结果由第一作者的情况下，高阶正切函子（$A = T^k K$）和情况下的喷气环（$A = K[X]/(X^{k+1})$）。我们调查这些一般的Weil函子的一些代数方面（“K-理论的Weil函子”，行动的“伽罗瓦群“$\Aut_K(A)$），这将是重要的后续应用一般微分几何。
英文摘要：
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.
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