论文标题
响环下的淤积理论
Silting theory under change of rings
论文作者
论文摘要
本文的主要目的是将$ r $ -Algebra $λ$的淤积理论与noetherian ring $ r $与其张量产品$λ\ otimesγ$与另一个$ r $ r $ -algebra $γ$的淤积理论进行比较。如果$ r $ -Algebra $λ$是noetherian，$ r $ a完整的本地戒指和$ \ mathfrak {a} $是环$ r $的一定理想，我们获得了$λ$的淤积poset和其商$λ\λ\ otimimes r/ \ m m m iantfrak的silting poset。此外，我们研究了这种培养的倾斜复合物的限制，并推断出代数$λ$的淤积嵌入和下降结果，以及某个代数$（λ\ otimesγ_i）_ {i \ in I} $中的代数$（λ\ otimiesγ_i）_ {i \。
The main goal of this paper is to compare the silting theory of an $R$-algebra $Λ$ over a Noetherian ring $R$ with that of its tensor product $Λ\otimes Γ$ with another $R$-algebra $Γ$. In the case that the $R$-algebra $Λ$ is Noetherian, $R$ a complete local ring and $\mathfrak{a}$ a certain ideal of the ring $R$, we obtain an isomorphism between the silting poset of $Λ$ and that of its quotient $Λ\otimes R/ \mathfrak{a}$. Furthermore, we study the restrictions of such a bijection to tilting complexes and deduce silting embedding and descent results for the algebra $Λ$ and a certain family of algebras $(Λ\otimes Γ_i)_{i \in I}$.
