论文标题
Grothendieck二元性和Greenlees-May双重性在分级戒指上
Grothendieck duality and Greenlees-May duality on graded rings
论文作者
论文摘要
我们为$ \ mathbb {z} $ - 分级环制定并证明Serre的等价。如果仅限于$ \ mathbb {n} $ - 分级戒指的通常情况时，我们的Serre对等效性版本也通过更自然的条件代替$ a_1 $ a_1 $生成$ a_1 $生成的条件来促进通常的戒指，以更自然的条件来使我们称之为Cartier条件。对于$ \ mathbb {z} $ - 来自翻转和拖鞋的分级环，这种卡地亚条件更自然地与所讨论的flip/flop的几何形状有关。我们还将Grothendieck二元性解释为Greenlees-May二重性的实例。这些构成了[YEU20A，YEU20B]中翻转和拖船同源研究的基本环境。
We formulate and prove Serre's equivalence for $\mathbb{Z}$-graded rings. When restricted to the usual case of $\mathbb{N}$-graded rings, our version of Serre's equivalence also sharpens the usual one by replacing the condition that $A$ be generated by $A_1$ over $A_0$ by a more natural condition, which we call the Cartier condition. For $\mathbb{Z}$-graded rings coming from flips and flops, this Cartier condition relates more naturally to the geometry of the flip/flop in question. We also interpret Grothendieck duality as an instance of Greenlees-May duality for graded rings. These form the basic setting for a homological study of flips and flops in [Yeu20a, Yeu20b].
