Continuity of the radius of convergence of differential equations on p-adic analytic curves
Continuity of the radius of convergence of differential equations on p-adic analytic curves
复制标题
p-adic解析曲线上微分方程收敛半径的连续性
DOI：
10.1007/s00222-010-0266-7
复制
发表时间：
2008
影响因子：
3.1
通讯作者：
F. Baldassarri
中科院分区：
文献类型：
--
作者：
F. Baldassarri
本文讨论非阿基米德，特别是p-adic，解析曲线的联系，在Berkovich的意义。曲线必须是紧的，但允许联络上有有限个亚纯奇点。对于曲线的半稳定形式模型的任何选择，我们定义了一个几何的，内在的概念，作为曲线上的函数的一组局部解的收敛半径的归一化，值在（0，1]。对于一个足够精细的选择的半稳定模型，我们证明了连续性，对数的线性和对数分段线性的功能。我们介绍和表征Robba连接，这是连接的层的解决方案是恒定的任何开放的磁盘中包含的曲线，正是因为它发生在经典的情况下。
This paper deals with connections on non-archimedean, especially 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 a geometric, intrinsic notion of normalized radius of convergence of a full set of local solutions as a function on the curve, with values in (0, 1]. For a sufficiently refined choice of the semistable model, we prove continuity, logarithmic concavity and logarithmic piece-wise linearity of that function. We introduce and characterize Robba connections, that is connections whose sheaf of solutions is constant on any open disk contained in the curve, precisely as it happens in the classical case.