Summer School of Mathematics "Berkovich Spaces"
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|Introduction to Berkovich Analytic Spaces (Lecture 1)|
Michael Temkin (Univ. Pennsylvania)
28 juin 2010
In this mini-course we will introduce Berkovich analytic spaces over a non-Archimedean field and will study their basic properties. A familiarity with algebraic geometry and commutative algebra is the main prerequisite for the course. Some familiarity with field valuations and formal schemes may also be helpful, though I will mention briefly the facts we will need about them. In order to cover the large amount of material we will concentrate on describing definitions and constructions and formulating the main results of the theory, although in some cases main ideas of the proofs will be outlined. The course will be divided into five parts as follows: §1 valuations, non-Archimedean fields and Banach algebras, §2 affinoid algebras and spaces, §3 analytic spaces, §4 connection to other categories: analytification of algebraic varieties and generic fiber of a formal scheme, §5 analytic curves.
– Lecture 1: June 28, 11:00
– Lecture 2: June 29, 09:00
– Lecture 3: June 29, 11:30
– Lecture 4: June 30, 11:30
– Lecture 5: July 1, 10h30
– Lecture 6: July 2, 09h00