AI 中文总结
该文针对Artin代数上的自正交τ-倾斜模，证明其零化子相关的Hom-正交性与有限维数障碍，将所得准则应用于根基平方为零的Artin代数及半单源三角矩阵代数，拓展了倾斜模理论的研究。
AI 中文摘要
设A为Artin代数，T为自正交τ-倾斜右A-模，令I=Ann_A(T)。我们证明：Hom_A(I,T)=0且对所有n≥1，Ext_A^n(I,T)=0。由此可得，由I生成的挠类与Sub T是Hom-正交的。这种分离可通过理想的顶、基座及投射支撑表示忠实性准则。我们还证明了一个有限维数障碍：若B=End_A(T)^op具有有限小有限维数，则Fac T∩⊥≥0T={0}。作为应用，自正交τ-倾斜猜想对根基平方为零的Artin代数成立。最后，支撑准则适用于具有任意局部末端块的半单源三角矩阵代数。
英文摘要
Let $A$ be an Artin algebra and let $T$ be a self-orthogonal $τ$-tilting right $A$-module. Set $I=\Ann_A(T)$. We prove that \[ \Hom_A(I,T)=0=\Ext_A^n(I,T)\qquad(n\geq 1). \] It follows that the torsion class generated by $I$ is Hom-orthogonal to $\Sub T$. This separation yields faithfulness criteria expressed through ideal tops, socles, and projective supports. We also prove a finitistic-dimension obstruction: if $B=\End_A(T)^{\rm op}$ has finite little finitistic dimension, then $\Fac T\cap{}^{\perp_{\geq0}}T=\{0\}$. As an application, the self-orthogonal $τ$-tilting conjecture holds for radical square zero Artin algebras. Finally, the support criteria apply to semisimple-source triangular matrix algebras with arbitrary local terminal blocks.
Comments12 pages, comments are welcome
