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Jet and prolongation spaces

Part of: Algebraic geometry: Foundations Differential and difference algebra

Published online by Cambridge University Press:  24 February 2010

Rahim Moosa  and
Thomas Scanlon
Rahim Moosa
Affiliation:
University of Waterloo, Department of Pure Mathematics, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada, ([email protected])
Thomas Scanlon
Affiliation:
University of California, Berkeley, Department of Mathematics, Evans Hall, Berkeley, CA 94720-3480, USA, ([email protected])
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Abstract

The notion of a prolongation of an algebraic variety is developed in an abstract setting that generalizes the difference and (Hasse) differential contexts. An interpolating map that compares these prolongation spaces with algebraic jet spaces is introduced and studied.

Keywords

differential fielddifference fieldjet spaceprolongationWeil restriction

MSC classification

Secondary: 12H99: None of the above, but in this section 14A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 2 , April 2010 , pp. 391 - 430
Copyright
Copyright © Cambridge University Press 2010

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References

1.Bosch, S., Lütkebohmert, W. and Raynaud, M., Néron models, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Volume 21 (Springer, 1990).Google Scholar
2.Buium, A., Geometry of differential polynomial functions, I, Algebraic groups. Am. J. Math. 115(6) (1993), 1385–1444.Google Scholar
3.Gillet, H., Differential algebra—a scheme theory approach, in Differential algebra and related topics (Newark, NJ, 2000), pp. 95–123 (World Scientific, 2002).Google Scholar
4.Grothendieck, A., Techniques de construction en géométrie analytique, VII, Étude locale des morphisme: éléments de calcul infinitésimal, Séminaire Henri Cartan, Volume 13(14) (L'École Normal Supérieure, Paris, 1960/1961).Google Scholar
5.Kantor, J. M., Formes et opérateurs différentiels sur les espaces analytiques complexes, Soc. Math. France Bull. Suppl. Mémoire 53 (1977), 5–80.CrossRefGoogle Scholar
6.Kolchin, E. R., Differential algebra and algebraic groups, Pure and Applied Mathematics, Volume 54 (Academic Press, 1973).Google Scholar
7.Moosa, R. and Scanlon, T., Generalised Hasse varieties and their jet spaces, preprint (2009).Google Scholar
8.Mustaţă, M., Jet schemes of locally complete intersection canonical singularities (with an appendix by David Eisenbud and Edward Frenkel), Invent. Math. 145(3) (2001), 397–424.CrossRefGoogle Scholar
9.Oesterlé, J., Nombres de Tamagawa et groupes unipotents en caractéristiques p, Invent. Math. 78(1) (1984), 13–88.CrossRefGoogle Scholar
10.Pillay, A. and Ziegler, M., Jet spaces of varieties over differential and difference fields, Selecta Math. 9(4) (2003), 579–599.Google Scholar
11.Scanlon, T., A model complete theory of valued D-fields, J. Symb. Logic 65(4) (2000), 1758–1784.CrossRefGoogle Scholar
12.Ziegler, M., Separably closed fields with Hasse derivations, J. Symb. Logic 68(1) (2003), 311–318.CrossRefGoogle Scholar