Continuity of the radius of convergence of differential equations on $p$-adic analytic curves
Abstract
This paper deals with connections on $p$-adic analytic curves, in the sense of Berkovich. The curves must be compact but the connections are allowed to have a finite number of meromorphic singularities on them. For any choice of a semistable formal model of the curve, we define an intrinsic notion of normalized radius of convergence as a function on the curve, with values in $(0,1]$. For a sufficiently refined choice of the semistable model, we prove continuity and logarithmic concavity of that function. We characterize \emph{Robba connections}, that is connections whose sheaf of solutions is constant on any open disk contained in the curve.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2008
- DOI:
- 10.48550/arXiv.0809.2479
- arXiv:
- arXiv:0809.2479
- Bibcode:
- 2008arXiv0809.2479B
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Number Theory;
- 12H25;
- 14G22
- E-Print:
- 51 pages, 4 figures