Mixed resolutions and simplicial sections. (English) Zbl 1143.14002
Let \(\mathbb{K}\)-be a field of characteristic zero. Given a morphism \(\pi : Z\to X\) of \(\mathbb{HK}\)-schemes, the author defines a simplicial section of \(\pi\) based on a covering of \(X\). Next, a de Rham and a simplicial- Čech typed resolution is mixed and a notion of a mixed resolution of a \(\mathcal{O}_X\)-modules is introduced.
A connection, used by the author [Adv. Math. 198, No. 1, 383–432 (2005; Zbl 1085.53081)], between those two notions is presented. The author believes that his results will be helpful in a proof of M. Kontsevich’s claim [Lett. Math. Phys. 66, No. 3, 157–216 (2003; Zbl 1058.53065)].
A connection, used by the author [Adv. Math. 198, No. 1, 383–432 (2005; Zbl 1085.53081)], between those two notions is presented. The author believes that his results will be helpful in a proof of M. Kontsevich’s claim [Lett. Math. Phys. 66, No. 3, 157–216 (2003; Zbl 1058.53065)].
Reviewer: Marek Golasiński (Toruń)
MSC:
| 14A15 | Schemes and morphisms |
| 13D02 | Syzygies, resolutions, complexes and commutative rings |
| 18E30 | Derived categories, triangulated categories (MSC2010) |
Keywords:
Čech resolution; Grothendieck connection; inverse system; \(\mathbb{K}\)-scheme; mixed resolution; sheaf; simplicial sectionReferences:
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