论文标题
投射品种和矢量束的穆斯丁模型
Mustafin models of projective varieties and vector bundles
论文作者
论文摘要
Mustafin品种是由Bruhat-tits建筑物中的积分点选择引起的投射空间的良好变性。在最近的工作中，安妮特·沃纳（Annette Werner）和作者通过算术几何形状开始研究了穆斯芬品种获得的平面曲线退化。此外，我们将这些技术应用于在平面曲线上构建矢量束模型，并具有强烈的半固定降低。在这项工作中，我们采取了一种研究射影品种退化的更普遍的问题。我们的方法包括确定格罗布纳基地在替换额上的行为，而不是独特的分解环。最后，当相应的投影变化是一条曲线时，我们概述了$ p- $ adic simpson通信的应用程序。
Mustafin varieties are well-studied degenerations of projective spaces induced by a choice of integral points in a Bruhat--Tits building. In recent work, Annette Werner and the author initiated the study of degenerations of plane curves obtained by Mustafin varieties by means of arithmetic geometry. Moreover, we applied these techniques to construct models of vector bundles on plane curves with strongly semistable reduction. In this work, we take a Groebner basis approach to the more general problem of studying degenerations of projective varieties. Our methods include determining the behaviour of Groebner bases under substitution over unique factorisation rings. Finally, we outline applications to the $p-$adic Simpson correspondence, when the respective projective variety is a curve.
