Parameter-test-ideals of Cohen–Macaulay rings
Parameter-test-ideals of Cohen–Macaulay rings
复制标题
科恩-麦考利环的参数检验理想
DOI：
10.1112/s0010437x07003417
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发表时间：
2007
影响因子：
1.8
通讯作者：
Mordechai Katzman
中科院分区：
文献类型：
--
作者：
Mordechai Katzman
摘要 我们描述了一种计算某些局部 Cohen-Macaulay 环中参数测试理想的算法。该算法基于对环残差场的射包的 Frobenius 图的研究以及 Sharp 的“特殊理想”概念的应用。我们的技术还提供了一种算法，用于计算环的顶部局部上同调模块及其留数场的单射外壳上的 Frobenius 作用的幂零指数。对残差场的射壳上的幂零元的研究也极大地简化了正特性 D 模生成器一文中著名结果的证明 (J. Alvarez-Montaner, M. Blickle 和 G. Lyubeznik, Math. Res. Lett. 12 (2005), 459–473)。
Abstract We describe an algorithm for computing parameter-test-ideals in certain local Cohen–Macaulay rings. The algorithm is based on the study of a Frobenius map on the injective hull of the residue field of the ring and on the application of Sharp’s notion of ‘special ideals’. Our techniques also provide an algorithm for computing indices of nilpotency of Frobenius actions on top local cohomology modules of the ring and on the injective hull of its residue field. The study of nilpotent elements on injective hulls of residue fields also yields a great simplification of the proof of the celebrated result in the article Generators of D-modules in positive characteristic (J. Alvarez-Montaner, M. Blickle and G. Lyubeznik, Math. Res. Lett. 12 (2005), 459–473).