**Contemporary Mathematics**

Volume: 571;
2012;
276 pp;
Softcover

MSC: Primary 14; 19; 11;

Print ISBN: 978-0-8218-5322-1

Product Code: CONM/571

List Price: $97.00

AMS Member Price: $77.60

MAA Member Price: $87.30

**Electronic ISBN: 978-0-8218-8987-9
Product Code: CONM/571.E**

List Price: $97.00

AMS Member Price: $77.60

MAA Member Price: $87.30

# Regulators

Share this page *Edited by *
*José Ignacio Burgos Gil; Rob de Jeu; James D. Lewis; Juan Carlos Naranjo; Wayne Raskind; Xavier Xarles*

This volume contains the proceedings of the Regulators
III Conference, held from July 12 to July 22, 2010, in Barcelona, Spain.

Regulators can be thought of as realizations from motivic cohomology, which
is very difficult to compute, to more computable theories such as Hodge, Betti,
l-adic, and Deligne cohomology. It is a very intricate subject that
thrives on its interaction with algebraic K-theory, arithmetic
geometry, number theory, motivic cohomology, Hodge theory and mathematical
physics.

The articles in this volume are a reflection of the various approaches to
this subject, such as results on motivic cohomology, descriptions of
regulators, a revisiting of a number of fundamental conjectures (such as new
results pertaining to the Hodge and standard conjectures), and more.

#### Readership

Graduate students and research mathematicians interested in number theory, K-theory, and algebraic geometry.

# Table of Contents

## Regulators

- Preface vii8 free
- Speakers and titles of talks ix10 free
- Quintic surface over 𝑝-adic local fields with infinite 𝑝-primary torsion in the Chow group of 0-cycles 112 free
- A remark on primitive cycles and Fourier-Radon transform 1930
- Remarks on Grothendieck’s standard conjectures 2536
- On the derivative of a normal function associated with a Deligne cohomology class 3344
- Quelques cas d’annulation du troisième groupe de cohomologie non ramifiée 4556
- Coniveau filtration and mixed motives 5162
- Around the Gysin triangle I 7788
- Regulators, entropy and infinite determinants 117128
- Secondary theories for étale groupoids 135146
- Introduction 135146
- 1. Elements of Chern-Weil theory for étale groupoids 136147
- 2. Multiplicative Cohomology and Differential Characters for étale groupoids 143154
- 3. Multiplicative K-theory for étale groupoids 145156
- 4. Characteristic classes for secondary theories associated to étale groupoids 148159
- References 150161

- Finite generation conjectures for motivic cohomology theories over finite fields 153164
- Le foncteur de filtration par le poids 167178
- K-Theory and G-Theory of DG-stacks 175186
- 1. Introduction. 175186
- 2. Fundamentals of the K-theory and G-theory of algebraic stacks 177188
- 3. Fundamentals of DG-stacks 181192
- 4. K-Theory of projective space bundles 192203
- 5. G-theory of dg-stacks: devissage, localization and homotopy property 199210
- 6. Cohomology and Homology theories for Dg-stacks 212223
- 7. Appendix A: Key theorems of Waldhausen K-theory 214225
- 8. Appendix B: Injective resolutions of dg-modules 215226
- References 216227

- Derived categories of coherent sheaves and motives of K3 surfaces 219230
- Serre-Tate parameters and Jacobian inversion for rigid Calabi-Yau 3-folds 233244
- An example concerning specialization of torsion subgroups of Chow groups 249260
- Motivic intersection complex 255266