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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Global $F$-regularity of Schubert varieties with applications to $\mathcal {D}$-modules
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by Niels Lauritzen, Ulf Raben-Pedersen and Jesper Funch Thomsen PDF
J. Amer. Math. Soc. 19 (2006), 345-355 Request permission

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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Additional Information
  • 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
  • Received by editor(s): February 18, 2004
  • Published electronically: December 2, 2005
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 19 (2006), 345-355
  • MSC (2000): Primary 32C38, 14B15
  • DOI: https://doi.org/10.1090/S0894-0347-05-00509-6
  • MathSciNet review: 2188129