Corpus ID: 119317989

Strong generators in $D^{perf}(X)$ and $D^b_{coh}(X)$

@article{Neeman2017StrongGI,
  title={Strong generators in \$D^\{perf\}(X)\$ and \$D^b\_\{coh\}(X)\$},
  author={Amnon Neeman},
  journal={arXiv: Algebraic Geometry},
  year={2017}
}
  • A. Neeman
  • Published 2017
  • Mathematics
  • arXiv: Algebraic Geometry
The only real change is that the statement - not the proof - of Lemma 1.5 has been changed to remove superfluous hypotheses. The old statement is given in the new Remark 1.6. The reason for the change is that, although for the current the generality of Remark 1.6 is ample, Lemma 1.5 is used again in the proof of Lemmas 2.2 and 2.3 of arXiv:1806.05777 and there the superfluous hypotheses of Remark 1.6 don't hold, we need Lemma 1.5 in the generality of its revised statement. 
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Strong generators in 𝐷_{𝑝𝑒𝑟𝑓}(𝑋) for schemes with a separator
This paper extends the result from Amnon Neeman regarding strong generators in Dperf(X), from X being a quasicompact, separated scheme to X being quasicompact, quasiseparated scheme that admits a… Expand
Annihilation of cohomology, generation of modules and finiteness of derived dimension
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Triangulated categories with a single compact generator and a Brown representability theorem
We generalize a theorem of Bondal and Van den Bergh. A corollary of our main results says the following: Let $X$ be a scheme proper over a noetherian ring $R$. Then the Yoneda map, taking an object… Expand
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We survey some recent results on strong generation in \({\mathbf D}^{\mathrm {perf}}(X)\) and \(\mathbf {D}^b_{\mathrm {coh}}(X)\).
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Grothendieck proved that if f: X ) Y is a proper morphism of nice schemes, then Rf* has a right adjoint, which is given as tensor product with the relative canonical bundle. The original proof was by… Expand
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