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

Wolfgang Bertram (1)

1 IECN - Institut Élie Cartan de Nancy

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}).

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

Domaines: Géométrie différentielle [math.DG]

Wolfgang Bertram. Simplicial Differential Calculus, Divided Differences, and Construction of Weil Functors. 2011. ⟨hal-00516973v2⟩