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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.

Number theory. --- Differential geometry. --- Algebraic geometry. --- Number Theory. --- Differential Geometry. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Differential geometry --- Number study --- Numbers, Theory of --- Algebra --- L-functions --- Functions, L --- -Number theory --- Funcions L --- Geometria diferencial --- Geometria --- Càlcul de tensors --- Connexions (Matemàtica) --- Coordenades --- Corbes --- Cossos convexos --- Dominis convexos --- Espais de curvatura constant --- Espais simètrics --- Estructures hermitianes --- Formes diferencials --- G-estructures --- Geodèsiques (Matemàtica) --- Geometria de Riemann --- Geometria diferencial global --- Geometria integral --- Geometria simplèctica --- Hiperespai --- Subvarietats (Matemàtica) --- Topologia diferencial --- Varietats (Matemàtica) --- Varietats de Kähler --- L-Funcions --- Teoria de nombres