Format:
1 Online-Ressource (XI, 299 p)
ISBN:
9781461200413
,
9781461265856
Series Statement:
Progress in Mathematics 218
Note:
The authors' initial aim in writing this book was to provide an English language version of the now out-of-print book Geometrie analytique rigide et applications. In attempting to simply update certain parts, we were compelled to rethink and refine others. Thus the book grew into a more voluminous, as well as a different, publication. Its main purpose remains, however, to provide an easy introduction to the theory of rigid spaces. There is a large number of exercises, offering specific examples as well as more specialized topics not treated in the main text. This theory has evolved over the last 20 years. Moreover, the appreciation for rigid spaces by researchers in algebraic geometry and number theory is growing. The introduction of rigid spaces by J. Tate had the purpose of describing degenerations of curves and abelian varieties. This theme has been studied and the theory is extended by many authors, e. g. , D. Mumford, V. Drinfel'd, Y. Manin, M. Raynaud, H. Grauert, R. Remmert, R. Kiehl, L. Gerritzen, S. Bosch et al. Newer applications, like the Langlands conjecture for function fields, the solution of Abhyankar's problem and rigid cohomology, provide a fruitful interaction between rigid spaces, number theory and algebraic geometry. Some chapters of this book give an introduction to these more advanced themes. As a consequence, the level of exposition (and of the exercises) in this book varies. We will now describe the contents of the various chapters
Language:
English
Keywords:
Algebraische Geometrie
;
Algebraische Mannigfaltigkeit
;
Analytische Stellenalgebra
;
Analytische Geometrie
DOI:
10.1007/978-1-4612-0041-3
URL:
Volltext
(lizenzpflichtig)
Author information:
Fresnel, Jean 1939-
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