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Regulators of canonical extensions

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Regulators of canonical extensions Geometry seminar University of Cambridge, October 31st, 2007 Carlos T. Simpson C.N.R.S., Laboratoire J. A. Dieudonne Universite de Nice-Sophia Antipolis

  • chow group

  • reznikov proves

  • group

  • chern

  • chern-simons regulators

  • deligne cohomology provides

  • rational coho


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Regulators of canonical extensions
Geometry seminar
University of Cambridge, October 31st,
Carlos T. Simpson
C.N.R.S.,LaboratoireJ.A.Dieudonne´ Universit´edeNice-SophiaAntipolis
2007
This is joint work with Jaya Iyer, starting from a talk she gave in Nice around 2004
Let X be a smooth projective variety, D = D 1 + . . . + D k a strict normal crossings divisor with smooth components. Put U := X D .
Suppose ( E r ) is a flat vector bundle on U . The usual Chern classes of E in rational coho-mology are zero.
It is not always the case that c i ( E ) = 0 in CH i ( X ) Q : the basic examples are flat line bundles on an abelian variety.
Esnault’s conjecture: if f : Y X is a fam-ily of varieties, then the flat bundle underlying R i f Q has Chern classes zero in the rational Chow groups.
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