Hypersurfaces in projective schemes and a moving lemma
| hal.structure.identifier | Institut des Hautes Études Scientifiques [IHES] | |
| dc.contributor.author | GABBER, Ofer | |
| hal.structure.identifier | Équipe Théorie des Nombres | |
| dc.contributor.author | LIU, Qing | |
| dc.contributor.author | LORENZINI, Dino | |
| dc.date.accessioned | 2024-04-04T02:18:14Z | |
| dc.date.available | 2024-04-04T02:18:14Z | |
| dc.date.created | 2011 | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0012-7094 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189294 | |
| dc.description.abstractEn | Let X/S be a quasi-projective morphism over an affine base. We develop in this article a technique for proving the existence of closed subschemes H/S of X/S with various favorable properties. We offer several applications of this technique, including the existence of finite quasi-sections in certain projective morphisms, and the existence of hypersurfaces in X/S containing a given closed subscheme C, and intersecting properly a closed set F. Assume now that the base S is the spectrum of a ring R such that for any finite morphism Z -> S, Pic(Z) is a torsion group. This condition is satisfied if R is the ring of integers of a number field, or the ring of functions of a smooth affine curve over a finite field. We prove in this context a moving lemma pertaining to horizontal 1-cycles on a regular scheme X quasi-projective and flat over S. We also show the existence of a finite surjective S-morphism to the projective space P_S^d for any scheme X projective over S when X/S has all its fibers of a fixed dimension d. | |
| dc.language.iso | en | |
| dc.publisher | Duke University Press | |
| dc.subject.en | Noether normalization | |
| dc.subject.en | Avoidance lemma | |
| dc.subject.en | Bertini-type theorem | |
| dc.subject.en | Hypersurface | |
| dc.subject.en | Moving lemma | |
| dc.subject.en | Multisection | |
| dc.subject.en | 1-cycle | |
| dc.subject.en | Pictorsion | |
| dc.subject.en | Quasi-section | |
| dc.subject.en | Rational equivalence | |
| dc.subject.en | Zero locus of a section | |
| dc.subject.en | Noether normalization. | |
| dc.title.en | Hypersurfaces in projective schemes and a moving lemma | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.identifier.arxiv | 1404.5366 | |
| bordeaux.journal | Duke Mathematical Journal | |
| bordeaux.page | 1187-1270 | |
| bordeaux.volume | 164 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 7 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00989236 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00989236v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Duke%20Mathematical%20Journal&rft.date=2015&rft.volume=164&rft.issue=7&rft.spage=1187-1270&rft.epage=1187-1270&rft.eissn=0012-7094&rft.issn=0012-7094&rft.au=GABBER,%20Ofer&LIU,%20Qing&LORENZINI,%20Dino&rft.genre=article |
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