Simplicial Differential Calculus, Divided Differences, and Construction of Weil Functors

Details Simplicial Differential Calculus, Divided Differences, and Construction of Weil Functors Simplicial Differential Calculus, Divided Differences, and Construction of Weil Functors

2010-09-13

arxiv.org/abs/1009.2354v2

Mathematics

Differential Geometry

V2: minor changes, and chapter 3: new results included; to appear in Forum Mathematicum

Scientific paper

We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules over a topological ring K. This calculus has the advantage that the number of evaluation points growths linearly with the degree, and not exponentially as in the classical, "cubic" approach. In particular, it is better adapted to the case of positive characteristic, where it permits to define Weil functors corresponding to scalar extension from K to truncated polynomial rings K[X]/(X^{k+1}).

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