论文标题
离散估值字段上双曲线曲线的最小日志常规模型
Minimal log regular models of hyperbolic curves over discrete valuation fields
论文作者
论文摘要
在著名的Deligne和Mumford的论文中，他们证明，当且仅当曲线的Jacobian品种在其估值环的残留场被代数关闭的情况下，曲线的雅各布品种稳定减少时，在离散估值领域的合适曲线会稳定。在证据中，最小规则模型的理论起着重要作用。在本文中，我们建立了最小曲线的最小对数模型的理论。作为该理论的关键工具，我们以$ 2 $维的本地方案给出了一个标准，就其最小的降低化而言是规则的。此外，作为该理论的应用，我们证明了上述等价性，而没有对残基领域的假设。
In the famous paper of Deligne and Mumford, they proved that a proper hyperbolic curve over a discrete valuation field has stable reduction if and only if the Jacobian variety of the curve has stable reduction in the case where the residue field of its valuation ring is algebraically closed. In the proof, the theory of minimal regular models played an important role. In this paper, we establish a theory of minimal log regular models of curves. As a key tool for this theory, we give a criterion for $2$-dimensional local schemes to be log regular in terms of their minimal desingularization. Moreover, as an application of this theory, we prove the above equivalence without the assumption on the residue field.
