Elliptic Curves, Modular Forms and Iwasawa Theory: In Honour of John H. Coates' 70th Birthday, Cambridge, UK, March 2015 (Springer Proceedings in Mathematics & Statistics (188))

Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory , held in honour of the 70 th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields. Front Matter....Pages i-viii Congruences Between Modular Forms and the Birch and Swinnerton-Dyer Conjecture....Pages 1-31 p-adic Measures for Hermitian Modular Forms and the Rankin–Selberg Method....Pages 33-86 Big Image of Galois Representations Associated with Finite Slope p-adic Families of Modular Forms....Pages 87-123 Behaviour of the Order of Tate–Shafarevich Groups for the Quadratic Twists of \(X_0(49)\) ....Pages 125-159 Compactifications of S-arithmetic Quotients for the Projective General Linear Group....Pages 161-223 On the Structure of Selmer Groups....Pages 225-252 Control of \(\Lambda \) -adic Mordell–Weil Groups....Pages 253-294 Some Congruences for Non-CM Elliptic Curves....Pages 295-309 Diophantine Geometry and Non-abelian Reciprocity Laws I....Pages 311-334 On p-adic Interpolation of Motivic Eisenstein Classes....Pages 335-371 Vanishing of Some Galois Cohomology Groups for Elliptic Curves....Pages 373-399 Coates–Wiles Homomorphisms and Iwasawa Cohomology for Lubin–Tate Extensions....Pages 401-468 Bigness in Compatible Systems....Pages 469-492 Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference __Elliptic Curves, Modular Forms and Iwasawa Theory__, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields.