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DESCRIPTION: Abstract:  We know that a Frobenius pull back of a semistable 
 bundle need not remain semistable. However\, if X is a nonsingular projecti
 ve curve of genus g and defined over a field of characterstic p &gt\; 0\, t
 hen Shepherd-Barron and X. Sun proved (independently)\, that for a semistab
 le vector bundle V of rank r\, the instability degree of F * V is bounded b
 y  2(g-1)(r-1).   This bound on the instability is useful in keeping a chec
 k on some of the  behaviour of a vector bundle afterFrobenius pullbacks.  F
 or example one can prove that\, for any vector bundle V and for large  p (i
 n terms of degree of X and rank of V)\, the Harder-Narasimhan filtration of
  F * V is a refinement of the  Frobenius pull back of the Harder-Narasimhan
  filtration of V.We give counterexamples to prove that some such conditions
  on p is necessary.    We extend such results to vector bundles over  highe
 r dimesional verieties.To prove these\, we answer a question/conjecture of 
 X. Sun (though  for p bigger than rank of E + dimension of X)\, which is an
  anaolgue  of  the above mentioned result of Shepherd-Barron and X. Sun in 
 higher dimension.   
DTSTAMP:20140108T112700
DTSTART:20140116T171500
CLASS:PUBLIC
LOCATION:Hörsaal 1\, Arnimallee 3
SEQUENCE:0
SUMMARY:Mathe. Kolloquium: Dr. Vijaya Trivedi (Mumbai / Berlin)
UID:33640897@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/math/dates/colloquium/Archiv-2014/16_01_14T
 rivedi.html
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