Arithmetic and Geometry

doi:10.1017/CBO9781316106877

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.

- Aa Reduce text
- Aa Enlarge text

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .

To save content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

Contents

Frontmatter
pp i-iv
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Contents
pp v-vi
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Preface
pp vii-viii
- By Luis V. Dieulefait, Universitat de Barcelona, Gerd Faltings, Max-Planck-Institut für Mathematik (Bonn), D. R. Heath-Brown, University of Oxford, Yu. I. Manin, Max-Planck-Institut für Mathematik, Boris Z. Moroz, Max-Planck-Institut für Mathematik (Bonn), Jean-Pierre Wintenberger, Université de Strasbourg
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Introduction
pp ix-ix
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

List of participants
pp x-xii
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Trimester Seminar
pp xiii-xxii
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Workshop on Serre's conjecture
pp xxiii-xxvii
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

The research conference
pp xxviii-xxxiv
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

1 - Galois groups of local fields, Lie algebras and ramification
pp 1-23
- By Victor Abrashkin, University of Durham
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

2 - A characterisation of ordinary modular eigenforms with CM
pp 24-35
- By Rajender Adibhatla, Universität Regensburg, Panagiotis Tsaknias, University of Luxembourg
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

3 - Selmer complexes and p-adic Hodge theory
pp 36-88
- By Denis Benois, Université de Bordeaux
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

4 - A survey of applications of the circle method to rational points
pp 89-113
- By Tim D. Browning, University of Bristol
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

5 - Arithmetic differential equations of Painlevé VI type
pp 114-138
- By Alexandru Buium, University of New Mexico, Yuri I. Manin, Max-Planck-Institut für Mathematik
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

6 - Differential calculus with integers
pp 139-187
- By Alexandru Buium, University of New Mexico
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

7 - Un calcul de groupe de Brauer et une application arithmétique
pp 188-192
- By Jean-Louis Colliot-Thélène, Université Paris-Sud
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

8 - Connectedness of Hecke algebras and the Rayuela conjecture: a path to functoriality and modularity
pp 193-216
- By Luis V. Dieulefait, Universitat de Barcelona, Ariel Pacetti, Universidad de Buenos Aires
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

9 - Big image of Galois representations and congruence ideals
pp 217-254
- By Haruzo Hida, UCLA, Los Angeles, Jacques Tilouine, Université Paris
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

10 - The skew-symmetric pairing on the Lubin–Tate formal module
pp 255-263
- By Mikhail A. Ivanov, Saint-Petersburg State University, Sergei V. Vostokov, University of St. Petersburg
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

11 - Equations in matrix groups and algebras over number fields and rings: prolegomena to a lowbrow noncommutative Diophantine geometry
pp 264-282
- By Boris Kunyavskiĭ, Bar-Ilan University
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

12 - On the l-adic regulator as an ingredient of Iwasawa theory
pp 283-317
- By Leonid V. Kuz'min, National Research Center Kurchatov Institute
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

13 - On a counting problem for G-shtukas
pp 318-350
- By Ngo Dac Tuan, Université de Paris
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

14 - Modular forms and Calabi-Yau varieties
pp 351-372
- By Kapil Paranjape, IISER, Mohali, India, Dinakar Ramakrishnan, Caltech
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

15 - Derivative of symmetric square p-adic L-functions via pull-back formula
pp 373-400
- By Giovanni Rosso, Université Paris
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

16 - Uniform bounds for rational points on cubic hypersurfaces
pp 401-421
- By Per Salberger, Chalmers University of Technology
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

17 - Descent on toric fibrations
pp 422-435
- By Alexei N. Skorobogatov, Imperial College London
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

18 - On filtrations of vector bundles over P1Z
pp 436-457
- By Aleksander Smirnov, Steklov Institute of Mathematics in St. Petersburg
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

19 - On the dihedral Euler characteristics of Selmer groups of Abelian varieties
pp 458-492
- By Jeanine Van Order, The Hebrew University of Jerusalem
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

20 - CM values of higher Green's functions and regularized Petersson products
pp 493-503
- By Maryna Viazovska, National University of Kyiv
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Metrics

Altmetric attention score

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

Arithmetic and Geometry

Book description

Refine List

Actions for selected content:

Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Introduction
pp ix-ix

List of participants
pp x-xii

Trimester Seminar
pp xiii-xxii

Workshop on Serre's conjecture
pp xxiii-xxvii

The research conference
pp xxviii-xxxiv

1 - Galois groups of local fields, Lie algebras and ramification
pp 1-23

2 - A characterisation of ordinary modular eigenforms with CM
pp 24-35

3 - Selmer complexes and p-adic Hodge theory
pp 36-88

4 - A survey of applications of the circle method to rational points
pp 89-113

5 - Arithmetic differential equations of Painlevé VI type
pp 114-138

6 - Differential calculus with integers
pp 139-187

7 - Un calcul de groupe de Brauer et une application arithmétique
pp 188-192

8 - Connectedness of Hecke algebras and the Rayuela conjecture: a path to functoriality and modularity
pp 193-216

9 - Big image of Galois representations and congruence ideals
pp 217-254

10 - The skew-symmetric pairing on the Lubin–Tate formal module
pp 255-263

11 - Equations in matrix groups and algebras over number fields and rings: prolegomena to a lowbrow noncommutative Diophantine geometry
pp 264-282

12 - On the l-adic regulator as an ingredient of Iwasawa theory
pp 283-317

13 - On a counting problem for G-shtukas
pp 318-350

14 - Modular forms and Calabi-Yau varieties
pp 351-372

15 - Derivative of symmetric square p-adic L-functions via pull-back formula
pp 373-400

16 - Uniform bounds for rational points on cubic hypersurfaces
pp 401-421

17 - Descent on toric fibrations
pp 422-435

18 - On filtrations of vector bundles over P1Z
pp 436-457

19 - On the dihedral Euler characteristics of Selmer groups of Abelian varieties
pp 458-492

20 - CM values of higher Green's functions and regularized Petersson products
pp 493-503

Metrics

Altmetric attention score

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information

Arithmetic and Geometry

Book description

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Altmetric attention score

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information