Arithmetic and geometry / [edited by] Luis Dieulefait...[et al.].

Papers presented at the trimestre on "Arithmetic and Geometry" at the Hausdor Research Institute for Mathematics (University of Bonn), January-April 2013.

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 Painleve 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 arithmetique Jean-Louis Colliot-Thelene;
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 Kunyavskii;
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.

In this proceedings volume leading authorities describe the state of the art in number theory, particularly Diophantine and arithmetic geometry. The book gives an excellent overview of the subject for graduate students and it is essential reading for researchers wishing to keep abreast of recent developments.