Talk:Coherent duality

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)

"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)

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

Given a S-scheme X, the trace morphism is

:$f\_*\; \backslash mathcal\{O\}\_X\; \backslash to\; \backslash mathcal\{O\}\_S$

{{Cite arxiv|title = Vanishing of the higher direct images of the structure sheaf|arxiv = 1404.1827 |date = 2014-04-07|first = Andre|last = Chatzistamatiou|first2 = Kay|last2 = Rülling}}

{{reflist-talk}}

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)