Proceedings Of A Conference On Local Fields

From July 25-August 6, 1966 a Summer School on Local Fields was held in Driebergen (the Netherlands), organized by the Netherlands Universities Foundation for International Cooperation (NUFFIC) with financial support from NATO. The scientific organizing Committl!e consisted ofF. VANDER BLIJ, A.H.M. LEVELT, A.F. MaNNA, J.P. MuRRE and T.A. SPRINGER. The Summer School was attended by approximately 80 mathematicians from various countries. The contributions collected in the present book are all based on the talks given at the Summer School. It is hoped that the book will serve the same purpose as the Summer School: to provide an introduction to current research in Local Fields and related topics. July 1967 T.A. SPRINGER Contents ARnN, M. and B. MAZUR: Homotopy of Varieties in the Etale Topology 1 BAss, H: The Congruence Subgroup Problem 16 BRUHAT, F. et J. TITs: Groupes algebriques simples sur un corps local . 23 CASSELS, J.W.S. : Elliptic Curves over Local Fields 37 DwoRK, B. : On the Rationality of Zeta Functions and L-Series 40 MaNNA, A.F. : Linear Topological Spaces over Non-Archimedean Valued Fields . 56 NERON, A. : Modeles minimaux des espaces principaux homo genes sur les courbes elliptiques 66 RAYNAUD, M. : Passage au quotient par une relation d'equivalence plate . 78 REMMERT, R. : Algebraische Aspekte in der nichtarchimedischen Analysis . 86 SERRE, J.-P. : Sur les groupes de Galois attaches aux groupes p-divisibles . 118 SWINNERTON-DYER, P. : The Conjectures of Birch and Swinnerton- Dyer, and of Tate . 132 TATE, J.T.

Casimir forces between spheres and loop integrals / J. Babington -- Analytic corrections to the electromagnetic Casimir interaction between a sphere and a plate at short distances / M. Bordag and V. Nikolaev -- Casimir physics : geometry, shape and material / T. Emig -- Semitransparent pistons / P. Morales and K. Kirsten -- Using boundary methods to compute the Casimir energy / F.C. Lombardo, F.D. Mazzitelli and P.I. Villar -- Electromagnetic non-contact gears : prelude / P. Parashar [und weitere] -- The scattering approach to the Casimir force / S. Reynaud [und weitere] -- Scalar Casimir energies for separable coordinate systems : application to semi-transparent planes in an annulus / J. Wagner, K.A. Milton and K. Kirsten -- Demonstrating the strong geometry dependence of the Casimir force on a surface with deep, nanoscale corrugations / H.B. Chan [und weitere] -- New results for the Casimir interaction : sample characterization and low temperature measurements / R.S. Decca, D. Lopez and E. Osquiguil -- Casimir force experiments in air : two birds with one stone / S. De Man [und weitere] -- Experimental features of the recent lateral Casimir force measurement / H.-C. Chiu and U. Mohideen -- Lateral Casimir-Polder force measurement using Bose Einstein condensates / G.A. Moreno -- Repulsive Casimir and van der Waals forces : from measurements to future technologies / J.N. Munday and F. Capasso -- Macroscopic quantum vacuum and microscopic gravitation / R. Onofrio -- The PVLAS experiment and its results : probing the quantum vacuum with polarized light and magnetic fields / F. Della Valle [und weitere] -- Thermal Casimir effect for conducting plates and the Bohr-van Leeuwen theorem / G. Bimonte -- Electromagnetic Casimir effect in wedge geometry and the energy-momentum tensor in media / I. Brevik, S.A. Ellingsen and K.A. Milton -- Casimir-Polder potential in thermal non-equilibrium / S.A. Ellingsen [und weitere] -- Geometry-temperature interplay in the Casimir effect / H. Gies and A. Weber -- Thermal effects in the magnetic Casimir-Polder interaction / H. Haakh, F. Intravaia and C. Henkel -- Mode contributions to the Casimir effect / F. Intravaia and C. Henkel -- Thermal Casimir force between magnetic materials / G.L. Klimchitskaya, B. Geyer and V.M. Mostepanenko -- The Casimir effect and the foundations of statistical physics / V.M. Mostepanenko and G.L. Klimchitskaya -- Casimir-Lifshitz forces and entropy / L.P. Pitaevskii -- The thermal Casimir effect : saturation / B.E. Sernelius -- Finite temperature Casimir effect in the presence of extra dimensions / L.P. Teo and K. Kirsten -- The role of magnetoplasmons in Casimir force calculations / R. Esquivel-Sirvent [und weitere] -- Suspended graphene films and their Casimir interaction with ideal conductor / I.V. Fialkovsky -- Casimir energy of finite width mirrors : renormalization, self-interaction limit and Lifshitz formula / I.V. Fialkovsky, V.N. Markov and Yu. M. Pis'mak -- Role of surface states in the Casimir force between semiconducting films / M. Govoni, C. Calandra and A. Benassi -- On the Casimir entropy between "perfect crystals" / C. Henkel and F. Intravaia -- Theory of the Casimir effect for gratings / V.N. Marachevsky