Differential forms on arithmetic jet spaces

Differential forms on arithmetic jet spaces

We study derivations and differential forms on the arithmetic jet spaces of smooth schemes, relative to several primes. As applications, we give a new interpretation of arithmetic Laplacians, and we discuss the de Rham cohomology of some specific arithmetic jet spaces, especially arithmetic jet spac...

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Veröffentlicht in:Selecta mathematica (Basel, Switzerland) Switzerland), 2011-06, Vol.17 (2), p.301-335
Hauptverfasser: Borger, James, Buium, Alexandru
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Beschreibung
Zusammenfassung:We study derivations and differential forms on the arithmetic jet spaces of smooth schemes, relative to several primes. As applications, we give a new interpretation of arithmetic Laplacians, and we discuss the de Rham cohomology of some specific arithmetic jet spaces, especially arithmetic jet spaces of linear tori, elliptic curves, and Kummer surfaces.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-010-0054-7