Overview

The 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern overview of the subject for graduate students in arithmetic geometry and Diophantine geometry. It is also essential reading for any researcher wishing to keep abreast of the latest developments in the field. Highlights include Tim Browning's survey on applications of the circle method to rational points on algebraic varieties and Per Salberger's chapter on rational points on cubic hypersurfaces.

Full Product Details

Author:   Luis Dieulefait (Universitat de Barcelona) ,  Gerd Faltings ,  D. R. Heath-Brown (University of Oxford) ,  Yu. V. Manin
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Volume:   420
Dimensions:   Width: 15.20cm , Height: 3.00cm , Length: 22.90cm
Weight:   0.760kg
ISBN:  

9781107462540

ISBN 10:   1107462541
Pages:   538
Publication Date:   08 October 2015
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Preface Luis Dieulefait, Gerd Faltings, D. R. Heath-Brown, Yuri I. Manin, B. Z. Moroz and Jean-Pierre Wintenberger; Introduction; List of participants; Trimester seminar; Workshop on the Serre conjecture; The research conference; 1. Galois groups of local fields, Lie algebras, and ramification Victor Abrashkin; 2. A characterisation of ordinary modular eigenforms with CM Rajender Adibhatla and Panagiotis Tsaknias; 3. Selmer complexes and p-adic Hodge theory Denis Benois; 4. A survey of applications of the circle method to rational points T. D. Browning; 5. Arithmetic differential equations of Painlevé VI type Alexandru Buium and Yuri I. Manin; 6. Differential calculus with integers Alexandru Buium; 7. Un calcul de groupe de Brauer et une application arithmétique Jean-Louis Colliot-Thélène; 8. Connectedness of Hecke algebras and the Rayuela conjecture: a path to functoriality and modularity Luis Dieulefait and Ariel Pacetti; 9. Big image of Galois representations and congruence ideals Haruzo Hida and Jacques Tilouine; 10. The skew-symmetric pairing on the Lubin–Tate formal module M. A. Ivanov and S. V. Vostokov; 11. Equations in matrix groups and algebras over number fields and rings: prolegomena to a lowbrow noncommutative Diophantine geometry Boris Kunyavskiĭ; 12. On the ℓ-adic regulator as an ingredient of Iwasawa theory L. V. Kuz'min; 13. On a counting problem for G-shtukas Ngo Dac Tuan; 14. Modular forms and Calabi–Yau varieties Kapil Paranjape and Dinakar Ramakrishnan; 15. Derivative of symmetric square p-adic L-functions via pull-back formula Giovanni Rosso; 16. Uniform bounds for rational points on cubic hypersurfaces Per Salberger; 17. Descent on toric fibrations Alexei N. Skorobogatov; 18. On filtrations of vector bundles over P1Z A. Smirnov; 19. On the dihedral Euler characteristics of Selmer groups of Abelian varieties Jeanine Van Order; 20. CM values of higher Green's functions and regularized Petersson products Maryna Viazovska.

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Author Information

Luis Dieulefait is Associate Professor in the Department of Algebra and Geometry at the University of Barcelona. D. R. Heath-Brown FRS is Professor of Pure Mathematics at the University of Oxford and has twice been an invited speaker at the International Congress of Mathematicians (ICM). He is one of a growing band of number theorists exploring the interface between analytic number theory and Diophantine geometry, which led him to co-organise the trimester of which this volume is the proceedings. Gerd Faltings is Managing Director of the Max Planck Institute for Mathematics in Bonn. Yuri I. Manin is Professor Emeritus at the Max Planck Institute for Mathematics in Bonn. B. Z. Moroz is Associate Professor at the Max Planck Institute for Mathematics in Bonn. Jean-Pierre Wintenberger is Professor at the Department of Mathematics at the University of Strasbourg.

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