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Grothendieck duality and Greenlees-May duality on graded rings | Wai-Kit Yeung
; | Date: |
23 Jan 2020 | Abstract: | 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]. | Source: | arXiv, 2001.8795 | Services: | Forum | Review | PDF | Favorites |
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