|Berkovich Spaces over Z (Lecture 1)|
Jérôme Poineau (Strasbourg)
7 juillet 2010
This course is divided into two parts.
• First, we shall recall Berkovich’s general construction of analytic spaces over Z with a particular emphasis on the affine line. It is a remarkable fact that in many respects this space behaves like usual analytic spaces: it is for instance Hausdorff, locally compact and locally path connected, and its local rings are Henselian, Noetherian, and regular.
• Second, we shall turn our attention to the study of Stein subsets of the affine line over Z. These subsets are defined in terms of the vanishing of coherent cohomology. We shall derive some applications of this study to the construction of convergent power series with integral coefficients having prescribed poles, and to the inverse Galois problem.
– Lecture 1: July 7, 11:30
– Lecture 2: July 8, 11:30
– Lecture 3: July 9, 10:30
|Jérôme Poineau (Strasbourg)|
Jérôme Poineau est maître de conférences en mathématiques à l’université de Strasbourg, membre de l’équipe de géométrie arithmétique.