Minimal log regular models of hyperbolic curves over discrete valuation fields

Autor:	Nagamachi, Ippei
Rok vydání:	2022
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry 11G20 14H25
Druh dokumentu:	Working Paper
Popis:	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. Comment: 50 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.11964 Zobrazit plný text záznamu View this record from Arxiv