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Harder-Narasimhan Filtrations which are not split by the Frobenius maps

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Title Harder-Narasimhan Filtrations which are not split by the Frobenius maps
 
Creator BHAUMIK, S
MEHTA, V
 
Subject Frobenius splitting
Borel-Weil-Bott theorem
strong Harder-Narasimhan Filtrations
 
Description We will produce a smooth projective scheme X over a"currency sign, a rank 2 vector bundle V on X with a line subbundle L having the following property. For a prime p, let F (p) be the absolute Fobenius of X (p) , and let L (p) aS,aEuro parts per thousand V (p) be the restriction of L aS,aEuro parts per thousand V. Then for almost all primes p, and for all t a parts per thousand yenaEuro parts per thousand 0, is a non-split Harder-Narasimhan filtration. In particular, is not a direct sum of strongly semistable bundles for any t. This construction works for any full flag veriety G/B, with semisimple rank of G a parts per thousand yenaEuro parts per thousand 2. For the construction, we will use Borel-Weil-Bott theorem in characteristic 0, and Frobenius splitting in characteristic p.
 
Publisher INDIAN ACAD SCIENCES
 
Date 2014-10-17T04:42:06Z
2014-10-17T04:42:06Z
2013
 
Type Article
 
Identifier PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 123(3)361-363
http://dx.doi.org/10.1007/s12044-013-0134-7
http://dspace.library.iitb.ac.in/jspui/handle/100/15976
 
Language en