Ordinary varieties and the comparison between multiplier ideals and test ideals
Ordinary varieties and the comparison between multiplier ideals and test ideals
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普通品种及乘数理想与检验理想的比较
DOI：
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发表时间：
2010
影响因子：
0.8
通讯作者：
V. Srinivas
中科院分区：
文献类型：
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作者：
M. Mustaţă;V. Srinivas
考虑如下猜想：如果X是特征为零的域k上的光滑不可约n维射影簇，则存在一个稠密的正特征约化集Xs，使得Frobenius态射在Hn（Xs，OXs）上的作用是双射的。还有另一个猜想有关某些不变量的奇异性的特征零（乘数理想）与不变量的积极特征（测试理想）。我们证明了在环境非奇异簇的情况下，前一个猜想蕴涵后一个猜想。
Abstract We consider the following conjecture: if X is a smooth and irreducible n-dimensional projective variety over a field k of characteristic zero, then there is a dense set of reductions Xs to positive characteristic such that the action of the Frobenius morphism on Hn(Xs, OXs ) is bijective. There is another conjecture relating certain invariants of singularities in characteristic zero (the multiplier ideals) with invariants in positive characteristic (the test ideals). We prove that the former conjecture implies the latter one in the case of ambient nonsingular varieties.