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Séminaire de Géométrie Algébrique du Bois Marie - 1966-67 - Théorie des intersections et théorÚme de
Riemann-Roch - (SGA 6) (Lecture notes in mathematics
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is not coherent, working with coherent sheaves has awkwardness (namely the kernel of a finite presentation can fail to be coherent). Because of this,
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Ben-Zvi, David; Francis, John; Nadler, David (2010), "Integral transforms and
Drinfeld centers in derived algebraic geometry",
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467:. If the complex consists only of the zero-th degree term, then it is pseudo-coherent if and only if it is so as a module.
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is a module that is perfect when it is viewed as a complex concentrated at degree zero. For example, if
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Kerz, Moritz; Strunk, Florian; Tamme, Georg (2018). "Algebraic K-theory and descent for blow-ups".
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Roughly speaking, a pseudo-coherent complex may be thought of as a limit of perfect complexes.
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has degree bounded above and consists of finite free modules in degree
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364:{\displaystyle L_{n}\to L_{n-1}\to \cdots \to L_{0}\to F\to 0}
487:(related notion; discussed at SGA 6 Exposé II, Appendix II.)
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108:-modules. They are also precisely the
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506:Ben-Zvi, Francis & Nadler (2010)
71:Perfect complexes are precisely the
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403:{\displaystyle {\mathcal {O}}_{X}}
248:{\displaystyle {\mathcal {O}}_{X}}
159:{\displaystyle {\mathcal {O}}_{X}}
123:is often called perfect; see also
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287:of finite type of length
135:When the structure sheaf
648:Inventiones Mathematicae
276:{\displaystyle n\geq 0}
177:By definition, given a
67:Other characterizations
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771:-related article is a
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615:. xii+700.
601:Luc Illusie
504:See, e.g.,
816:Categories
661:1611.08466
492:References
375:A complex
53:Noetherian
554:0805.0157
452:≥
425:→
356:→
350:→
337:→
334:⋯
331:→
323:−
312:→
291:; i.e.,
268:≥
474:See also
666:Bibcode
639:0354655
579:2202294
571:2669705
255:-module
119:over a
24:over a
22:modules
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440:where
767:This
690:(PDF)
656:arXiv
575:S2CID
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223:, an
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