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摘要翻译：
设X是X的射影簇，$\sigma$是X的自同构，L是X上的$\sigma$-满可逆丛，Z是X的闭子方案。在扭曲齐次坐标环$B=B(X,L,\sigma)$内，设I是B的截面在Z上消失的右理想。在Z和$\sigma$上的温和条件下，R是B中I的理想化器：B的极大子环，其中I是双边理想。给出了Z和$\sigma$的几何条件，证明了如果Z和$\sigma$在某种意义上是足够一般的，那么R是左和右noetherian的，具有有限的左和右上同调维数，是强右noetherian但不是强左noetherian的，满足右$\chi_d$（其中d=\codim Z)但不满足左$\chi_1$。我们还给出了右上同调维数为无穷大的右noetherian环的一个例子，部分回答了Stafford和Van den Bergh的一个问题。这推广了Rogalski在Z是$\mathbb{P}^d$中的一个点的情况下的结果。
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英文标题：
《Geometric idealizers》
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作者：
Susan J. Sierra
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Rings and Algebras 环与代数
分类描述：Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups
非交换环与代数，非结合代数，泛代数与格论，线性代数，半群
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let X be a projective variety, $\sigma$ an automorphism of X, L a $\sigma$-ample invertible sheaf on X, and Z a closed subscheme of X. Inside the twisted homogeneous coordinate ring $B = B(X, L, \sigma)$, let I be the right ideal of sections vanishing at Z. We study the subring R = k + I of B. Under mild conditions on Z and $\sigma$, R is the idealizer of I in B: the maximal subring of B in which I is a two-sided ideal. We give geometric conditions on Z and $\sigma$ that determine the algebraic properties of R, and show that if Z and $\sigma$ are sufficiently general, in a sense we make precise, then R is left and right noetherian, has finite left and right cohomological dimension, is strongly right noetherian but not strongly left noetherian, and satisfies right $\chi_d$ (where d = \codim Z) but fails left $\chi_1$. We also give an example of a right noetherian ring with infinite right cohomological dimension, partially answering a question of Stafford and Van den Bergh. This generalizes results of Rogalski in the case that Z is a point in $\mathbb{P}^d$.
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PDF链接：
https://arxiv.org/pdf/0809.3971
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