Hypersurfaces in projective schemes and a moving lemma

DOI10.1215/00127094-2877293zbMath1432.14002arXiv1404.5366OpenAlexW1805421763WikidataQ124831687 ScholiaQ124831687MaRDI QIDQ2352762

Qing Liu, Dino J. Lorenzini, Ofer Gabber

Publication date: 6 July 2015

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.5366

zbMATH Keywords

hypersurfacemoving lemmaNoether normalizationrational equivalenceBertini-type theoremzero locus of a section\(1\)-cycleavoidance lemmapictorsionquasisection

Mathematics Subject Classification ID

Arithmetic ground fields (finite, local, global) and families or fibrations (14D10) Fibrations, degenerations in algebraic geometry (14D06) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Algebraic cycles (14C25) Schemes and morphisms (14A15)

Related Items

Experiments on the Brauer map in high codimension, Grothendieck–Serre in the quasi-split unramified case, Finite morphisms to projective space and capacity theory, Pseudo-Néron model and restriction of sections, Codimension \(1\) foliations with numerically trivial canonical class on singular spaces, Complete intersections: moduli, Torelli, and good reduction, Global Weierstrass equations of hyperelliptic curves, Algebraic Spivak's theorem and applications, Nisnevich local good compactifications, Bertini theorems revisited, Rational points on generic marked hypersurfaces, Boundedness in families with applications to arithmetic hyperbolicity, Ramification theory of reciprocity sheaves. I: Zariski-Nagata purity, Demailly's notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps, The index of an algebraic variety, The Lang–Vojta Conjectures on Projective Pseudo-Hyperbolic Varieties, Arithmetic hyperbolicity: automorphisms and persistence, Non-Archimedean hyperbolicity and applications, Reduction type of smooth plane quartics, A probabilistic approach to systems of parameters and Noether normalization, Macaulayfication of Noetherian schemes, Purity of reciprocity sheaves, Interpolation over \(\mathbb{Z}\) and torsion in class groups, Good rings and homogeneous polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Smooth hypersurface sections containing a given subscheme over a finite field
• Trivialisation des modules projectifs. La méthode de Kronecker
• Module equivalences: Local to global. When primitive polynomials represent units
• Le formalisme du résultant. (The formalism of resultant)
• A class of projective modules which are nearly free
• Vector bundles over affine surfaces
• Unramified Skolem problems and unramified arithmetic Bertini theorems in positive characteristic
• On non-projective normal surfaces
• Projectivity of complete moduli
• A theorem on splitting of algebraic vector bundles and its applications
• On the Picard group: Torsion and the kernel induced by a faithfully flat map
• The index of an algebraic variety
• Finite morphisms to projective space and capacity theory
• On a special class of Dedekind domains
• The irreducibility of the space of curves of a given genus
• Introduction to Grothendieck duality theory
• About Euclidean rings
• \(S\)-units and \(S\)-class group in algebraic function fields
• Bertini theorems over finite fields
• Beiträge zur Arithmetik kommutativer Integritätsbereiche. VIII. Multiplikativ abgeschlossene Systeme von endlichen Idealen
• The Zero Locus of the Infinitesimal Invariant
• On the imbedding of a non-singular variety in an irreducible complete intersection
• On the Valuations Centered in a Local Domain
• On the representation of fields as finite unions of subfields
• Deformations of Algebraic Schemes
• Arithmetic over the rings of all algebraic integers.
• Vector Bundles and Projective Modules
• Projective Modules Over Rings with Many Units
• Strong Bertini Theorems
• Néron Models
• Courbes sur un trait et morphismes de contraction.
• The $K_2$ of rings with many units
• Bertini theorems for hypersurface sections containing a subscheme
• Geometric Invariant Theory
• Polynomial Maps of Affine Quadrics
• Geometric families of constant reductions and the Skolem property
• More étale covers of affine spaces in positive characteristic
• Projectivité des schémas en courbes sur un anneau de valuation discrète
• Moduli of curves with non-abelian level structure
• Approximation Theory and the Rank of Abelian Varieties Over Large Algebraic Fields
• Bezout Domains and Elliptic Curves
• Autour de la platitude
• Lectures on Curves on an Algebraic Surface. (AM-59)
• Groups Covered By Permutable Subsets