Abstract
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School “Berkovich spaces” at Institut de Mathématiques de Jussieu.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
V. Berkovich, Spectral Theory and Analytic Geometry Over Non-Archimedean Fields. Mathematical Surveys and Monographs, vol. 33 (American Mathematical Society, Providence, RI, 1990)
V. Berkovich, Étale cohomology for non-Archimedean analytic spaces. Publ. Math. IHES 78, 7–161 (1993)
V. Berkovich, Non-Archimedean analytic spaces, lecture notes, Trieste, 2009, available at http://www.wisdom.weizmann.ac.il/~vova/Trieste_2009.pdf
V. Berkovich, Smooth p-adic analytic spaces are locally contractible. Invent. Math. 137, 1–84 (1999)
S. Bosch, U. Güntzer, R. Remmert, Non-Archimedean Analysis. A Systematic Approach to Rigid Analytic Geometry (Springer, Berlin-Heidelberg-New York, 1984)
B. Conrad, Several approaches to non-archimedean geometry, in p-adic Geometry, University Lecture Series, vol. 45 (American Mathematical Society, Providence, RI, 2008)
B. Conrad, M. Temkin, Descent for non-archimedean analytic spaces. Available at http://www.math.huji.ac.il/~temkin/papers/Descent.pdf
A. Ducros, Variation de la dimension d’un morphisme analytique p-adique. Compositio Math. 143, 1511–1532 (2007)
A. Ducros, Les espaces de Berkovich sont excellents. Annales de l’institut Fourier 59, 1443–1552 (2009)
E. Hrushovski, F. Loeser, Non-archimedean tame topology and stably dominated types. arXiv:1009.0252v2
R. Kiehl, Der Endlichkeitssatz für eigentliche Abbildungen in der nichtarchimedischen Funktionentheorie. Inv. Math. 2, 191–214 (1967)
W. Lütkebohmert, Formal-algebraic and rigid-analytic geometry. Math. Ann. 286, 341–371 (1990)
M. Temkin, On local properties of non-Archimedean spaces. Math. Ann. 318, 585–607 (2000)
M. Temkin, On local properties of non-Archimedean spaces II. Isr. J. Math. 140, 1–27 (2004)
M. Temkin, A new proof of the Gerritzen-Grauert theorem. Math. Ann. 333, 261–269 (2005)
M. Temkin, Stable modifications of relative curves. J. Alg. Geom. 19, 603–677 (2010)
M. Temkin, Inseparable local uniformization. J. Algebra 373, 65–119 (2013)
Acknowledgements
I want to thank A. Ducros for careful reading of the notes and making many valuable comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Temkin, M. (2015). Introduction to Berkovich Analytic Spaces. In: Ducros, A., Favre, C., Nicaise, J. (eds) Berkovich Spaces and Applications. Lecture Notes in Mathematics, vol 2119. Springer, Cham. https://doi.org/10.1007/978-3-319-11029-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-11029-5_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11028-8
Online ISBN: 978-3-319-11029-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)