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THE DRINFELD–GRINBERG–KAZHDAN THEOREM IS FALSE FOR SINGULAR ARCS

Part of: Local theory Birational geometry

Published online by Cambridge University Press:  15 September 2015

David Bourqui  and
Julien Sebag
David Bourqui
Affiliation:
Institut de recherche mathématique de Rennes, UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France (david.bourqui@univ-rennes1.fr; julien.sebag@univ-rennes1.fr)
Julien Sebag
Affiliation:
Institut de recherche mathématique de Rennes, UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France (david.bourqui@univ-rennes1.fr; julien.sebag@univ-rennes1.fr)
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Abstract

In this note, we prove that the Drinfeld–Grinberg–Kazhdan theorem on the structure of formal neighborhoods of arc schemes at a nonsingular arc does not extend to the case of singular arcs.

Keywords

arc schemecurve singularity

MSC classification

Primary: 14E18: Arcs and motivic integration 14B05: Singularities
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 16 , Issue 4 , September 2017 , pp. 879 - 885
Copyright
© Cambridge University Press 2015 

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References

Bourqui, D. and Sebag, J., The Drinfeld–Grinberg–Kazhdan’s theorem and singularity theory, preprint (submitted).Google Scholar
Bruschek, C. and Hauser, H., Arcs, cords, and felts – six instances of the linearization principle, Amer. J. Math. 132(4) (2010), 941–986.Google Scholar
Bruschek, C., Mourtada, H. and Schepers, J., Arc spaces and the Rogers–Ramanujan identities, Ramanujan J. 30(1) (2013), 9–38.Google Scholar
Drinfeld, V., On the Grinberg–Kazhdan formal arc theorem, preprint.Google Scholar
Grinberg, M. and Kazhdan, D., Versal deformations of formal arcs, Geom. Funct. Anal. 10(3) (2000), 543–555.Google Scholar
Kolchin, E. R., On the exponents of differential ideals, Ann. of Math. (2) 42 (1941), 740–777.CrossRefGoogle Scholar
Levi, H., On the structure of differential polynomials and on their theory of ideals, Trans. Amer. Math. Soc. 51 (1942), 532–568.Google Scholar
O’Keefe, K. B., A property of the differential ideal y p , Trans. Amer. Math. Soc. 94 (1960), 483–497.CrossRefGoogle Scholar
Reguera, A. J., Towards the singular locus of the space of arcs, Amer. J. Math. 131(2) (2009), 313–350.Google Scholar
Ritt, J. F., Differential Algebra, American Mathematical Society Colloquium Publications, Vol. XXXIII (American Mathematical Society, New York, NY, 1950).Google Scholar
Stein, W. A. et al. , Sage Mathematics Software (Version 6.7) (The Sage Development Team, 2015). http://www.sagemath.org.Google Scholar