Thick subcategories on curves

关于稳定导出范畴的厚子范畴的一个注记

A note on thick subcategories of stable derived categories

对于具有足够多投射对象的正合范畴，我们建立了包含投射对象的厚子范畴与稳定导出范畴的厚子范畴之间的双射.使用这种双射，我们分类厚的子类别的有限生成模在当地的完整的交叉和生产的类别的相干层的一个单独的诺特计划与一个丰富的家庭的发电机。

Prime thick subcategories on elliptic curves

We classify all prime thick subcategories in the derived category of coherent sheaves on elliptic curves, and determine the Serre invariant locus of Matsui spectrum of derived category of coherent sheaves on any smooth projective curves.

Prime thick subcategories and spectra of derived and singularity categories of noetherian schemes

For an essentially small triangulated category $\mathcal{T}$, we introduce the notion of prime thick subcategories and define the spectrum of $\mathcal{T}$, which shares the basic properties with the spectrum of a tensor triangulated category introduced by Balmer. We mainly focus on triangulated categories that appear in algebraic geometry such as the derived and the singularity categories of a noetherian scheme $X$. We prove that certain classes of thick subcategories are prime thick subcategories of these triangulated categories. Furthermore, we use this result to show that certain subspaces…

加权射影曲线上的厚子类别与交换代数中旗形表示的 nilpotent 表示

Thick subcategories on weighted projective curves and nilpotent representations of quivers

本文研究加权射影曲线的导出范畴中厚子类别的结构，证明任何厚子类别要么等价于某些旗形的 nilpotent 表示导出范畴，要么是 torsion sheaves 的正交补，同时探讨了加权射影线的 admissible 子类别的生成条件及 Jordan-Holder 性质。

非交换曲线的容许子范畴

Admissible subcategories of noncommutative curves

该研究针对光滑非交换曲线导出范畴的容许子范畴展开，证明其仍为光滑非交换曲线的导出范畴，据此分类半正交分解、排除幻影范畴存在性，并将Bondal-Orlov重建定理推广到轨形曲线。

曲线上向量丛模的导出范畴中的容许子范畴

Admissible subcategories in derived categories of moduli of vector bundles on curves

我们证明了庞加莱丛给出了一个完全忠实的嵌入从一个曲线的导出范畴足够高的亏格到导出范畴的模空间的丛的秩$r$与固定的行列式的程度1。此外，我们表明，扭曲的嵌入，连同2个例外的线丛，给出了开始的半正交分解。这推广了Narasimhan和Fonarev-Kuznetsov的结果，他们嵌入了曲线的单个副本的导出范畴，秩为2。