论文标题
地图的展开，稳定地图上的第一个结果以及Mather-Yau/Gaffney-Hauser类型的结果
Unfoldings of maps, the first results on stable maps, and results of Mather-Yau/Gaffney-Hauser type in arbitrary characteristic
论文作者
论文摘要
考虑（正式/分析/代数）地图图（x，（k^p，o））。令G为右/联系/左右转换组。我将以下（经典）结果从真实/复杂分析的情况扩展到任意场k的情况。 *可分离的展开是本地微不足道的。 *展开是本地的IFF，它是无限的文献。 *零特征中MAP-GERMS分解的标准。 *仿射基础上展开的琐碎标准。 *将k孔振动成a-orbits。 *图是本地稳定的IFF，它是无限稳定的。 *稳定的地图是其基因型的未代。 *稳定的地图由其本地代数确定。 * Mather-Yau/Scherk/Gaffney-Hauser类型的结果。模块t^1_g f或相关代数如何确定f的g率类型？
Consider the (formal/analytic/algebraic) map-germs Maps(X,(k^p,o)). Let G be the group of right/contact/left-right transformations. I extend the following (classical) results from the real/complex-analytic case to the case of arbitrary field k. * A separable unfolding is locally trivial iff it is infinitesimally trivial. * An unfolding is locally versal iff it is infinitesimally versal. * The criterion of factorization of map-germs in zero characteristic. * Criteria of trivialization of unfoldings over affine base. * Fibration of K-orbits into A-orbits. * A map is locally stable iff it is infinitesimally stable. * Stable maps are unfodings of their genotypes. * Stable maps are determined by their local algebras. * Results of Mather-Yau/Scherk/Gaffney-Hauser type. How does the module T^1_G f, or related algebras, determine the G-equivalence type of f?
