This book is an outgrowth of the conference "Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods" that was held in Paris in May 2016. Gathering contributions by leading experts in the field ranging from original surveys to pure research articles, this volume provides comprehensive coverage of the front most developments in the field of regulator maps. Key topics covered are:

. Additive polylogarithms

. Analytic torsions

. Chabauty-Kim theory

. Local Grothendieck-Riemann-Roch theorems

. Periods

. Syntomic regulator

The book contains contributions by M. Asakura, J. Balakrishnan, A. Besser, A. Best, F. Bianchi, O. Gregory, A. Langer, B. Lawrence, X. Ma, S. Müller, N. Otsubo, J. Raimbault, W. Raskin, D. Rössler, S. Shen, N. Triantafi llou, S. Ünver and J. Vonk.

Klappentext

This book is an outgrowth of the conference Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods that was held in Paris in May 2016. Gathering contributions by leading experts in the field ranging from original surveys to pure research articles, this volume provides comprehensive coverage of the front most developments in the field of regulator maps. Key topics covered are:

• Additive polylogarithms

• Analytic torsions

• Chabauty-Kim theory

• Local Grothendieck-Riemann-Roch theorems

• Periods

• Syntomic regulator

The book contains contributions by M. Asakura, J. Balakrishnan, A. Besser, A. Best, F. Bianchi, O. Gregory, A. Langer, B. Lawrence, X. Ma, S. Müller, N. Otsubo, J. Raimbault, W. Raskin, D. Rössler, S. Shen, N. Triantafi llou, S. Ünver and J. Vonk.

Inhalt
Preface.- Regulator of hypergeometric fibrations.- Two recent p-adic approaches towards the (effective) Mordell conjecture.- The syntomic regulator for K2 of curves with arbitrary reduction.- Toric regulators.- Higher displays arising from filtered de Rham-Witt complexes.- Orbifold submersion and analytic torsions.- Analytic torsions, regulators and arithmetic hyperbolic manifolds.- A local re nement of the Adams-Riemann-Roch theorem in degree one.- Analytic torsion and dynamical flow: a survey on the Fried conjecture.- A survey of the additive dilogarithm.