The FFRT property of two-dimensional normal graded rings and orbifold curves
The FFRT property of two-dimensional normal graded rings and orbifold curves
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二维正态渐变环和环折曲线的FFRT性质
DOI：
10.1016/j.aim.2020.107215
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发表时间：
2020
影响因子：
1.7
通讯作者：
Ohkawa Ryo
中科院分区：
文献类型：
--
作者：
Hara Nobuo;Ohkawa Ryo
本文研究了有限F-表示型(简记为F-表示)。利用代数堆叠理论中的概念，得到了特征p>；0中二维正规分次环R的性质。给定一个分次环R，我们考虑一条奥氏曲线C，它是光滑曲线C=投影环R上的根叠，使得R是与C上的线丛L相关的截面环。然后，关于奥比诺曲线C上的Frobenius Push-Forward F⁎e(L I)，改写了R的Firt性质。结果，我们看到，如果R的奇点不是对数终端的，则R只有在特征p除以C的权的特殊情况下才有Firt。
We study the finite F-representation type (abbr. FFRT) property of a two-dimensional normal graded ring R in characteristic p> 0, using notions from the theory of algebraic stacks. Given a graded ring R, we consider an orbifold curve C, which is a root stack over the smooth curve C= Proj R, such that R is the section ring associated with a line bundle L on C. The FFRT property of R is then rephrased with respect to the Frobenius push-forwards F⁎ e (L i) on the orbifold curve C. As a result, we see that if the singularity of R is not log terminal, then R has FFRT only in exceptional cases where the characteristic p divides a weight of C.