Skip to Main Content

Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Essentially finite vector bundles on varieties with trivial tangent bundle
HTML articles powered by AMS MathViewer

by Indranil Biswas, A. J. Parameswaran and S. Subramanian PDF
Proc. Amer. Math. Soc. 139 (2011), 3821-3829 Request permission

Abstract:

Let $X$ be a smooth projective variety, defined over an algebraically closed field of positive characteristic, such that the tangent bundle $TX$ is trivial. Let $F_X : X \longrightarrow X$ be the absolute Frobenius morphism of $X$. We prove that for any $n \geq 1$, the $n$–fold composition $F^n_X$ is a torsor over $X$ for a finite group–scheme that depends on $n$. For any vector bundle $E \longrightarrow X$, we show that the direct image $(F^n_X)_*E$ is essentially finite (respectively, $F$–trivial) if and only if $E$ is essentially finite (respectively, $F$–trivial).
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14L15, 14F05
  • Retrieve articles in all journals with MSC (2010): 14L15, 14F05
Additional Information
  • Indranil Biswas
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
  • MR Author ID: 340073
  • Email: indranil@math.tifr.res.in
  • A. J. Parameswaran
  • Affiliation: Kerala School of Mathematics, Kunnamangalam (PO), Kozhikode, Kerala 673571, India
  • Email: param_aj@yahoo.com
  • S. Subramanian
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
  • Email: subramnn@math.tifr.res.in
  • Received by editor(s): March 22, 2010
  • Received by editor(s) in revised form: September 15, 2010, and September 16, 2010
  • Published electronically: March 15, 2011
  • Communicated by: Lev Borisov
  • © Copyright 2011 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3821-3829
  • MSC (2010): Primary 14L15, 14F05
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10804-9
  • MathSciNet review: 2823029