Regulators of canonical extensions

Sophia Antipolis

Description

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

Sujets

• Antipolis
• Chow ring

Informations

• Publié par: pefav
• Nombre de lectures: 8
• Langue: English

Extrait

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.