Affine Noetherian algebras, filtrations and presentations

Algebras without noetherian filtrations

We provide examples of finitely generated noetherian PI algebras for which there is no finite dimensional filtration with a noetherian associated graded ring; thus we answer negatively a question raised by M. Lorenz.

Presentations for subrings and subalgebras of finite co-rank

Let $K$ be a commutative Noetherian ring with identity, let $A$ be a $K$-algebra, and let $B$ be a subalgebra of $A$ such that $A/B$ is finitely generated as a $K$-module. The main result of the paper is that $A$ is finitely presented (resp. finitely generated) if and only if $B$ is finitely presented (resp. finitely generated). As corollaries we obtain: a subring of finite index in a finitely presented ring is finitely presented; a subalgebra of finite co-dimension in a finitely presented algebra over a field is finitely presented (already shown by Voden in 2009). We also discuss the role of …

Tilting 复形与交换诺特环上的余维数函数

Tilting complexes and codimension functions over commutative noetherian rings

本文在交换诺特环的导出范畴中，利用局部上同调构造与 sp-滤过关联的 silting 对象，并刻画其成为 tilting 的条件，特别与余维数函数及 Cohen-Macaulay 环同态像相关，同时给出 cosilting 对偶结果。

Quadratic algebras of skew type and the underlying semigroups

We consider algebras over a field K defined by a presentation K <x_1,..., x_n : R >, where $R$ consists of n choose 2 square-free relations of the form x_i x_j = x_k x_l with every monomial x_i x_j, i different from j, appearing in one of the relations. Certain sufficient conditions for the algebra to be noetherian and PI are determined. For this, we prove more generally that right noetherian algebras of finite Gelfand-Kirillov dimension defined by homogeneous relations satisfy a polynomial identity. The structure of the underlying monoid, defined by the same presentation, is described. This i…

关于诺特路径代数上t-结构的望远镜猜想

Telescope conjecture for t-structures over noetherian path algebras

本文证明了诺特路径代数导出范畴中同伦破碎t-结构均为紧生成，并用素谱到非交叉划分滤过偏序集的同态完整刻画了紧生成t-结构，正则环下还描述了宽子范畴。

关于局部环上滤法空间的几何学

On the geometry of spaces of filtrations on local rings

研究局部环上滤法空间的几何特性，引入一种度量并探讨其几何性质，结合牛顿-奥科诺夫体分析滤法空间结构，并研究对数canonical阈值函数的半连续性。