Uniform Annihilators of Systems of parameters

具有有限Cousin上同调的模具有一致局部上同调零化子

Modules with Finite Cousin Cohomologies Have Uniform Local Cohomological Annihilators

设A是诺特环.证明了任意具有有限Cousin复上同调的有限克鲁尔维数的A-模M存在一致的局部上同调零化子.对于满足（S_2）的有限模M，当M在具有Cohen-Macaulay形式纤维的局部环上时，上述逆定理也成立.

局部上同调一致零化子

Uniform annihilators of local cohomology

本文研究了具有一致零化子的诺特环的性质。事实证明，所有这些环应该是普遍悬链线和局部等维的。我们给出了这类环的一个充要条件，证明了如果环R是有限维Cohen-Macaulay环的象，则R有局部上同调的一致零化子.此外，我们还对关于维数不超过5的优环的猜想[Hu，猜想2.13]给出了肯定的回答。

Annihilators of $D$-modules in mixed characteristic

Let $R$ be a polynomial or formal power series ring with coefficients in a DVR $V$ of mixed characteristic with a uniformizer $π$. We prove that the $R$-module annihilator of any nonzero $\D(R,V)$-module is either zero or is generated by a power of $π$. In contrast to the equicharacteristic case, nonzero annihilators can occur; we give an example of a top local cohomology module of the ring $\mathbb{Z}_2[[x_0, \ldots, x_5]]$ that is annihilated by $2$, thereby answering a question of Hochster in the negative.

局部上同调零化子与Macaulay化

Local cohomology annihilators and Macaulayfication

研究了局部环上的局部上同调零化子与Macaulay化和算术Macaulay化之间的深层联系。局部上同调零化子通过p-标准参数系的概念出现。对于局部环，我们证明了Macaulayfictions存在性的等价性; p-标准参数系的存在性;是科恩-麦考利局部环的商;以及Faltings零化子定理的验证。对于纯忠实的有限生成模，证明了算术Macaulayfication的存在性与p-标准参数系的存在性的等价性，并证明了这两者等价于基环上算术Macaulayfication的存在性. Macaulayfication和普遍catenaricity之间的连接进行了讨论。

Annihilators of Koszul Homologies and Almost Complete Intersections

In this article, we propose a question on the annihilators of positive Koszul homologies of a system of parameters of an almost complete intersection $R$. The question can be stated in terms of the acyclicity of certain (finite) residual approximation complexes whose $0$-th homologies are the residue field of $R$. We show that our question has an affirmative answer for the first Koszul homology of any almost complete intersection, as well as for all positive Koszul homologies of certain system of parameters which exist in some almost complete intersection rings with small multiplicities. The s…

Residual Intersections and the Annihilator of Koszul Homologies

Cohen-Macaulayness, unmixedness, the structure of the canonical module and the stability of the Hilbert function of algebraic residual intersections are studied in this paper. Some conjectures about these properties are established for large classes of residual intersections without restricting local number of generators of the ideals involved. A family of approximation complexes for residual intersections is constructed to determine the above properties. Moreover some general properties of the symmetric powers of quotient ideals are determined which were not known even for special ideals with…