论文标题
$ k^b（proj（λ））$ $ n $ - 末端淤积络合物$
$n$-term silting complexes in $K^b(proj(Λ))$
论文作者
论文摘要
令$λ$为artin代数，$ k^b（proj（λ））$为$ proj（λ）中有界的共同链络合物的三角类别。$，众所周知，$ k^b（proj（λ））$中$ k^b（proj（λ））$ the $ the $τ$τ$ tix $ tixtintut tintut tintut tintut tiftti tifting理论描述。本文的目的是对$ k^b（proj（λ））$中的某些$ n $ term Silting络合物进行表征，这些络合物由$λ$ -Modules诱导。为此，我们介绍了$τ_n$ -rigid的概念，$τ_n$ -tilting和$τ_{n，m} $ - 倾斜$λ$ -Modules。后者既是$τ$ tilting and tilting in $ mod（λ）的概括。$也被陈述并证明了一些变体，用于$τ_n$的模块，是众所周知的bazzoni倾斜模块的特征。我们在$ k^b（proj（λ））$和$τ_n$ -rigid $λ$ -Modules中提供了一些连接。此外，给出了一个表征，以了解$τ_n$ - tilting $λ$ -MODULE是$ n $ tilting。我们还更深入地研究了$τ_{n，m} $ - 倾斜$λ$ - 模型及其作为$ m $的连接的属性。我们将开发的$τ_{n，m} $ - 倾斜理论应用于$λ的有限维度。$最后，在论文的结尾，我们讨论并陈述了一些我们认为对$τ_{n，m} $倾斜理论的未来发展至关重要的开放问题（猜想）。
Let $Λ$ be an Artin algebra and $K^b(proj(Λ))$ be the triangulated category of bounded co-chain complexes in $proj(Λ).$ It is well known that two-terms silting complexes in $K^b(proj(Λ))$ are described by the $τ$-tilting theory. The aim of this paper is to give a characterization of certain $n$-term silting complexes in $K^b(proj(Λ))$ which are induced by $Λ$-modules. In order to do that, we introduce the notions of $τ_n$-rigid, $τ_n$-tilting and $τ_{n,m}$-tilting $Λ$-modules. The latter is both a generalization of $τ$-tilting and tilting in $mod(Λ).$ It is also stated and proved some variant, for $τ_n$-tilting modules, of the well known Bazzoni's characterization for tilting modules. We give some connections between $n$-terms presilting complexes in $K^b(proj(Λ))$ and $τ_n$-rigid $Λ$-modules. Moreover, a characterization is given to know when a $τ_n$-tilting $Λ$-module is $n$-tilting. We also study more deeply the properties of the $τ_{n,m}$-tilting $Λ$-modules and their connections of being $m$-tilting in some quotient algebras. We apply the developed $τ_{n,m}$-tilting theory to the finitistic dimension of $Λ.$ Finally, at the end of the paper we discuss and state some open questions (conjectures) that we consider crucial for the future develop of the $τ_{n,m}$-tilting theory.
