Title: On a p-adic version of Narasimhan and Seshadri's theorem Show Chinese title

Title: 关于p进制Narasimhan和Seshadri定理的一个版本

Abstract: Consider a smooth projective curve C of genus g over a complete discrete valuation field of characteristic 0 and residue field \Fbar_p. Motivated by Narasimhan and Seshadri's theorem, Faltings asked whether all semistable vector bundles of degree 0 over C_{\C_p} are in the image of the p-adic Simpson correspondence. Works of Deninger-Werner and Xu show that this is equivalent for the vector bundle to having potentially strongly semistable reduction. We prove that if C has good reduction, p>r(r-1) (g-1) and we consider a vector bundle of rank r with stable reduction, the conditions of having potentially strongly semistable reduction and of having strongly semistable reduction are equivalent. In particular, we provide a negative answer to Faltings' question Show Chinese abstract

Abstract: 考虑一个在特征为0的完备离散赋值域上的光滑射影曲线C，其剩余域为\Fbar _p。 受Narasimhan和Seshadri定理的启发，Faltings询问是否所有度为0的C_{\C _p}上的半稳定向量丛都在p进Simpson对应之下。 Deninger-Werner和Xu的工作表明，这等价于该向量丛具有潜在强半稳定约化。 我们证明，如果C有良约化，p>r(r-1)(g-1)，并且我们考虑一个秩为r且具有稳定约化的向量丛，则具有潜在强半稳定约化和具有强半稳定约化的条件是等价的。 特别地，我们对Faltings的问题提供了否定回答。