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This quantity is the results of a (mainly) educational convention on mathematics geometry, held from July 30 via August 10, 1984 on the collage of Connecticut in Storrs. This quantity comprises accelerated models of virtually all of the tutorial lectures given through the convention. as well as those expository lectures, this quantity incorporates a translation into English of Falt­ ings' seminal paper which supplied the muse for the convention. We thank Professor Faltings for his permission to put up the interpretation and Edward Shipz who did the interpretation. We thank the entire those that spoke on the Storrs convention, either for aiding to make it a profitable assembly and allowing us to post this quantity. we might specially prefer to thank David Rohrlich, who added the lectures on top features (Chapter VI) whilst the second one editor used to be inevitably detained. as well as the editors, Michael Artin and John Tate served at the organizing committee for the convention and masses of the luck of the convention used to be as a result of them-our thank you visit them for his or her information. eventually, the convention was once purely made attainable via beneficiant provides from the Vaughn origin and the nationwide technology starting place.

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