Motives, Polylogarithms and Hodge Theory (Part II: Hodge Theory)
Edited by: Fedor Bogomolov & Ludmil Katzarkov
ISBN:1-57146-091-8
Year Published:
2002
Page: 334
Binding:
Hardcover
Price: $65
(or $100 for a set consisting of both Part 1 and 2)
Description
The present
volume contains papers of the participants in the International Press
Conference
on Motives, polylogarithms and non-abelian Hodge theory
which took
place at UC Irvine in June 1998. The conference commemorated
the
twentieth anniversary of the remarkable
"Higher regulators, algebraic K-theory and zeta functions of
elliptic curves". The conference presented some of the best recent research in algebraic
K-theory, Hodge theory, motivic cohomology
and polylogarithms. The research program of the
conference was organized around three main lecture series:
VladimirVoevodsky taught a minicourse overviewing
the recent developments in motivic cohomology and motivic homotopy theory; Don Zagier
lectured on new results describing the periods of holomorphic
and non-holomorphic modular forms; and Carlos Simpson
lectured on the theory of geometric n-stacks and its applications to the variational aspects of non-abelian
Hodge theory.
Table of Contents
III HODGE THEORY
Algebraic aspects of higher nonabelian Hodge
theory,
By Carlos Simpson
1 Introduction
2 Varieties with abelian
fundamental group
3 Nonabelian cohomology
4 Zoology
5 Cartesian families and base change
6 Very presentable n-stacks
7 Geometric n-stacks
8 Formal groupoids
of smooth type
9 Formal categories related to Hodge
theory
10 Presentability
and geometricity results
Higgs bundles, integrability, and holomorphic forms
By Donu Arapura
1 Consequences of the abelian theory
2 Higgs bundles and all that
3 A Nonabelian
Analogue of b1 = 2q
4 Quaternionic
geometry and Lagrangian maps
5 Integrability
of Hitchin'smap
6 Cohomology
support loci
7 Characteristic Cones and Products
of Higgs Bundles
8 Shafarevich
Maps
9 Powers of the canonical bundle
Nonabelian (p, p) classes,
by Ludmil Katzarkov and Tony Pantev
1 Introduction
2 Preliminaries on D-varieties
3 Nonabelian
Hodge structures
4 The Gauss-Manin
connection
5 The main theorem
Appendix A. Tangent stacks
The structure of Kahler groups, I: second cohomology,
by Alexander Reznikov
0 Introduction
1 A geometric picture for rigid
representations
2 Proof of the Superrigidity
Lemma
3 Variation of Hodge structure,
corresponding to
rigid representations to SO(2, n)
4 Variations of Hodge structure,
corresponding to a rigid representation
to Sp(4)
5 Variations of Hodge structure,
corresponding to a rigid representation
to Sp(2n), and proof of the Superrigidity Lemma (3)
6 Regulators, I: proof of the Main
Theorem
7 Regulators, II: proof of Theorems
0.1, 0.2
8 Nonrigid
representations
9 Three-manifolds groups are not Kahler
10 Central extensions of lattices in PSU(2, 1)
11 Smooth hypersurfaces
in ball quotients which are not K (π,1)
Some Hodge theory from Lie algebras,
by Constantin
Teleman
Introduction
1 Refresher on cyclic homology
2 Homology of gl(A)
3 Conjectures and some results for g(A)
4
5 Hodge-to de Rham
spectral sequence for X