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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Global $ F$-regularity of Schubert varieties with applications to $ \mathcal{D}$-modules


Authors: Niels Lauritzen, Ulf Raben-Pedersen and Jesper Funch Thomsen
Journal: J. Amer. Math. Soc. 19 (2006), 345-355
MSC (2000): Primary 32C38, 14B15
Published electronically: December 2, 2005
MathSciNet review: 2188129
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Abstract: We prove that Schubert varieties are globally $ F$-regular in the sense of Karen Smith. We apply this result to the category of equivariant and holonomic $ {\mathcal{D}}$-modules on flag varieties in positive characteristic. Here recent results of Blickle are shown to imply that the simple $ {\mathcal{D}}$-modules coincide with local cohomology sheaves with support in Schubert varieties. Using a local Grothendieck-Cousin complex, we prove that the decomposition of local cohomology sheaves with support in Schubert cells is multiplicity free.


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Niels Lauritzen
Affiliation: Institut for matematiske fag, Aarhus Universitet, Ny Munkegade, DK-8000 Århus, C Denmark
Email: niels@imf.au.dk

Ulf Raben-Pedersen
Affiliation: Institut for matematiske fag, Aarhus Universitet, Ny Munkegade, DK-8000 Århus, C Denmark
Email: ab061278@imf.au.dk

Jesper Funch Thomsen
Affiliation: Institut for matematiske fag, Aarhus Universitet, Ny Munkegade, DK-8000 Århus, C Denmark
Email: funch@imf.au.dk

DOI: http://dx.doi.org/10.1090/S0894-0347-05-00509-6
PII: S 0894-0347(05)00509-6
Received by editor(s): February 18, 2004
Published electronically: December 2, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.