Talk:Coherent duality

Please

Please convert all math to use the math tags. The formulas are unreadable on some browsers otherwise. You can use (almost) all LaTeX code inside math tags. --141.20.53.108 16:01, 3 November 2005 (UTC)[reply]

small comment

"the dualizing sheaf in the Cohen-Macaulay case" - yes, but only if a dualizing complex exists. It is possible that a Cohen-Macaulay ring will not have a dualizing complex, and hence, will not have a dualizing module. Maybe it should be cleared. 85.64.96.38 (talk) 23:11, 27 November 2009 (UTC)[reply]

(The material here will probably appear in the "coherent duality" article.)

Given a S-scheme X, the trace morphism is

f_{*}{\mathcal {O}}_{X}\to {\mathcal {O}}_{S}

^[1]

References

^ Chatzistamatiou, Andre; Rülling, Kay (2014-04-07). "Vanishing of the higher direct images of the structure sheaf". arXiv:1404.1827.

the pseudofunctor

f^! is not the pseudofunctor. D^+_QCoh is. https://stacks.math.columbia.edu/tag/0AU3 Fourier-Deligne Transgirl (talk) 01:52, 2 April 2025 (UTC)[reply]

[1] Chatzistamatiou, Andre; Rülling, Kay (2014-04-07). "Vanishing of the higher direct images of the structure sheaf". arXiv:1404.1827.

[1]