Arithmetic Geometry Lectures given at the C.I.M.E. Summer School hel
Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties over arbitrary rings, in particular over non-algebraically closed fields. It lies at the intersection between classical algebraic geometry
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2009
C.I.M.E. means Centro Internazionale Matematico Estivo, that is, International Mathematical Summer Center. Conceived in the early fifties, it was born in 1954 and made welcome by the world mathematical community where it remains in good health and spirit. Many mathematicians from all over the world have been involved in a way or another in C.I.M.E.’s activities during the past years. So they already know what the C.I.M.E. is all about. For the benefit of future potential users and co-operators the main purposes and the functioning of the Centre may be summarized as follows: every year, during the summer, Sessions (three or four as a rule) on different themes from pure and applied mathematics are offered by application to mathematicians from all countries. Each session is generally based on three or four main courses (24−30 hours over a period of 6−8 working days) held from specialists of international renown, plus a certain number of seminars. A C.I.M.E. Session, therefore, is neither a Symposium, nor just a School, but maybe a blend of both. The aim is that of bringing to the attention of younger researchers the origins, later developments, and perspectives of some branch of live mathematics. The topics of the courses are generally of international resonance and the participation of the courses cover the expertise of different countries and continents. Such combination, gave an excellent opportunity to young participants to be acquainted with the most advanced research in the topics of the courses and the possibility of an interchange with the world famous specialists. The full immersion atmosphere of the courses and the daily exchange among participants are a first building brick in the edifice of international collaboration in mathematical research. C.I.M.E. Director Pietro ZECCA Dipartimento di Energetica “S. Stecco” Universit`a di Firenze Via S. Marta, 3 50139 Florence Italy e-mail: [email protected]
C.I.M.E. Secretary Elvira MASCOLO Dipartimento di Matematica “U. Dini” Universit`a di Firenze viale G.B. Morgagni 67/A 50134 Florence Italy e-mail: [email protected]
For more information see CIME’s homepage: http://www.cime.unifi.it CIME activity is carried out with the collaboration and financial support of: – INdAM (Istituto Nazionale di Alta Matematica)
Jean-Louis Colliot-Th´el`ene Peter Swinnerton-Dyer Paul Vojta
Arithmetic Geometry Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10–15, 2007 Editors: Pietro Corvaja Carlo Gasbarri
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Authors Prof. Jean-Louis Colliot-Th´el`ene Universit´e Paris-Sud XI CNRS Labo. Math´ematiques Orsay 91405 CX Bˆatiment 425 France [email protected]
Prof. Peter Swinnerton-Dyer University of Cambridge Dept. of Pure Math. & Math. Statistics Wilberforce Road CB30WB Cambridge United Kingdom [email protected]
Prof. Paul Vojta University of California, Berkeley Department of Mathematics 970, Evans Hall Berkeley, CA 94720-3840 USA [email protected]
Editors Prof. Pietro Corvaja Universit`a di Udine Dipto. di Mat
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