论文标题
Noetherian代数的倾斜和淤积理论
Tilting and silting theory of noetherian algebras
论文作者
论文摘要
我们开发了Noetherian代数$λ$的淤积理论，而Noetherian ring $ r $。我们研究了$ 2 $ - $λ$的$ 2 $ - 末端淤积络合物的突变理论，因此，我们看到存在突变。与有限维代数一样，如果$ r $完全是本地，则有限的$λ$的有限扭转类对应于Silting $λ$ -Modules。我们显示的还原定理为$λ$的$ 2 $ term Silting络合物，并且通过使用该定理，我们研究了$λ$的模块类别的扭转类。当$ r $具有krull尺寸1时，我们通过使用有限维数代数的扭转类别来描述$λ$的扭转类。
We develop silting theory of a noetherian algebra $Λ$ over a commutative noetherian ring $R$. We study mutation theory of $2$-term silting complexes of $Λ$, and as a consequence, we see that mutation exists. As in the case of finite dimensional algebras, functorially finite torsion classes of $Λ$ bijectively correspond to silting $Λ$-modules, if $R$ is complete local. We show a reduction theorem of $2$-term silting complexes of $Λ$, and by using this theorem, we study torsion classes of the module category of $Λ$. When $R$ has Krull dimension one, we describe the set of torsion classes of $Λ$ explicitly by using the set of torsion classes of finite dimensional algebras.
