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Simplicial differential calculus, divided differences, and construction of Weil functors
-
Wolfgang Bertram
Published/Copyright:
January 3, 2013
Abstract.
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 
.
This calculus has the advantage
that the number of evaluation points grows 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 to truncated polynomial rings 
.
Keywords: Divided differences; differential calculus; jet functor; scalar extension; Weil functor; Taylor expansion
Received: 2010-11-04
Revised: 2011-01-03
Published Online: 2013-01-03
Published in Print: 2013-01-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Divided differences;
differential calculus;
jet functor;
scalar extension;
Weil functor;
Taylor expansion
Articles in the same Issue
- Masthead
- Isomorphism criteria for Witt rings of real fields
- Simplicial differential calculus, divided differences, and construction of Weil functors
- Rank 3 permutation characters and maximal subgroups
- On the oscillation and nonoscillation of the solutions of impulsive differential equations of second order with retarded argument
- A note on the existence of transition probability densities of Lévy processes
- Carleson measures and Logvinenko–Sereda sets on compact manifolds
- Cofiniteness of composed local cohomology modules
- Real hypersurfaces of type (A) in complex two-plane Grassmannians related to the commuting shape operator
- Deconstructibility and the Hill Lemma in Grothendieck categories
