摘要翻译:
在Berkovich意义下,我们考虑了光滑形式p-adic格式Cx的一般纤维Cx_{eta}中的解析区域U上具有可积连接(\Ce,\na)的向量丛。定义了U在xi\in U处的\emph{diameter}\delta_{\cx}(\xi,U),xi\in\cx_{\eta}点的\emph{radius}\rho{\cx}(\xi),R(\xi)=R_{\cx}(\xi,U,(\ce,\na))解的\emph{收敛半径}。我们讨论了这些函数关于Berkovich拓扑的(半)连续性。特别地,我们在一定的假设下证明了\delta_{\cx}(\xi,U)、\rho_{\cx}(\xi)和R_{\xi}(U,\ce,\na)是\xi的上半连续函数;对于仿射空间中的Laurent域,\delta_{\cx}(-,U)是连续的。在解析仿射线的仿射域U的经典情况下,R是连续函数。
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英文标题:
《Continuity of the radius of convergence of p-adic differential equations
on Berkovich analytic spaces》
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作者:
Francesco Baldassarri, Lucia Di Vizio
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Number Theory 数论
分类描述:Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数,丢番图方程,解析数论,代数数论,算术几何,伽罗瓦理论
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
We consider a vector bundle with integrable connection (\cE,\na) on an analytic domain U in the generic fiber \cX_{\eta} of a smooth formal p-adic scheme \cX, in the sense of Berkovich. We define the \emph{diameter} \delta_{\cX}(\xi,U) of U at \xi\in U, the \emph{radius} \rho_{\cX}(\xi) of the point \xi\in\cX_{\eta}, the \emph{radius of convergence} of solutions of (\cE,\na) at \xi, R(\xi) = R_{\cX}(\xi, U,(\cE, \na)). We discuss (semi-) continuity of these functions with respect to the Berkovich topology. In particular, under we prove under certain assumptions that \delta_{\cX}(\xi,U), \rho_{\cX}(\xi) and R_{\xi}(U,\cE,\na) are upper semicontinuous functions of \xi; for Laurent domains in the affine space, \delta_{\cX}(-,U) is continuous. In the classical case of an affinoid domain U of the analytic affine line, R is a continuous function.
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PDF链接:
https://arxiv.org/pdf/0709.2008