Cycles, derived categories, and rationality (Q4636227)

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scientific article; zbMATH DE number 6863807

Language	Label	Description	Also known as
English	Cycles, derived categories, and rationality	scientific article; zbMATH DE number 6863807

Statements

scholarly article

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Marcello Bernardara

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publication date

23 April 2018

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full work available at URL

https://arxiv.org/abs/1612.02415

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MaRDI profile type

MaRDI publication profile

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arXiv classification

math.AG

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Torification and factorization of birational maps

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On two rationality conjectures for cubic fourfolds

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Hodge theory and derived categories of cubic fourfolds

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Cubic fourfolds fibered in sextic del Pezzo surfaces

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Derived categories of Burniat surfaces and exceptional collections

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Algebraization of formal moduli. II: Existence of modifications

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Some Elementary Examples of Unirational Varieties Which are Not Rational

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Surjectivity of the total Clifford invariant and Brauer dimension

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Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields

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Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems

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Cubic fourfolds containing a plane and a quintic del Pezzo surface

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The transcendental lattice of the sextic Fermat surface

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Universal Unramified Cohomology of Cubic Fourfolds Containing a Plane

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Quadric surface bundles over surfaces

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The Brauer Group of a Commutative Ring

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On the derived categories of degree \(d\) hypersurface fibrations

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Rational equivalence of zero cycles for some more surfaces with \(p_ g=0\)

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Surfaces of general type with geometric genus zero: a survey

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Variétés de Prym et jacobiennes intermédiaires

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The Lüroth Problem

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Stably rational non rational varieties

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A semiorthogonal decomposition for Brauer-Severi schemes

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Derived categories and rationality of conic bundles

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Categorical representability and intermediate Jacobians of Fano threefolds

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Homological projective duality for determinantal varieties

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From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives

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The universal Euler characteristic for varieties of characteristic zero

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Gersten's conjecture and the homology of schemes

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Remarks on Correspondences and Algebraic Cycles

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THE BRAUER GROUP OF QUOTIENT SPACES BY LINEAR GROUP ACTIONS

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On the derived category of the classical Godeaux surface

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On the Jordan-Hölder property for geometric derived categories

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Determinantal Barlow surfaces and phantom categories

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Some loci of rational cubic fourfolds

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REPRESENTATION OF ASSOCIATIVE ALGEBRAS AND COHERENT SHEAVES

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REPRESENTABLE FUNCTORS, SERRE FUNCTORS, AND MUTATIONS

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ENHANCED TRIANGULATED CATEGORIES

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Reconstruction of a variety from the derived category and groups of autoequivalences

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Equivalences of Triangulated Categories and Fourier-Mukai Transforms

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Connexité rationnelle des variétés de Fano

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Torsion orders of complete intersections

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Exceptional collections on Dolgachev surfaces associated with degenerations

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The intermediate Jacobian of the cubic threefold

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Formes quadratiques multiplicatives et variétés algébriques

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Formes quadratiques multiplicatives et variétés algébriques : deux compléments

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A finiteness theorem for the Chow group of zero-cycles of a linear algebraic group on a \(p\)-adic field

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Galois descent on the second Chow group: development and applications

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Cycles de codimension 2 et<i>H</i><sup>3</sup>non ramifié pour les variétés sur les corps finis

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Variétés unirationelles non rationelles: Au-delà de l'exemple d'Artin et Mumford. (Non rational unirational varieties: Beyond the Artin-Mumford example)

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Hypersurfaces quartiques de dimension 3 : non-rationalité stable

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\(K_2\)-cohomology and the second Chow group

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La $R$-équivalence sur les tores

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Fibres quadratiques et composantes connexes réelles

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Unramified cohomology and the entire Hodge conjecture

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Enumerating exceptional collections of line bundles on some surfaces of general type

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Rationality in families of threefolds

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Relèvements modulo \(p^ 2\) et décomposition du complexe de de Rham. (Lifting modulo \(p^ 2\) and decomposition of the de Rham complex)

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Varieties over a finite field with trivial Chow group of 0-cycles have a rational point

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Sulle forme cubiche dello spazio a cinque dimensioni contenenti rigate razionali del \(4^\circ\) ordine

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Rational equivalence on singular varieties

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Exceptional collections of line bundles on the Beauville surface

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Derived categories of Keum's fake projective planes

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EXCEPTIONAL BUNDLES ON SURFACES WITH A MOVING ANTICANONICAL CLASS

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Exceptional vector bundles on projective spaces

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Geometric phantom categories

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Families of rationally connected varieties

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Cubic Fourfolds, K3 Surfaces, and Rationality Questions

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Stable rationality and conic bundles

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Cremona transformations and derived equivalences of K3 surfaces

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Rational curves on holomorphic symplectic fourfolds.

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On stable rationality of Fano threefolds and del Pezzo fibrations

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Exceptional sequences of invertible sheaves on rational surfaces

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Derived categories of Artin-Mumford double solids

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On nodal Enriques surfaces and quartic double solids

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The derived category of coherent sheaves on a quadric

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On standard norm varieties

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A vanishing theorem on fake projective planes with enough automorphisms

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Nonrational Hypersurfaces

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Rational connectedness and boundedness of Fano manifolds

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A remark on the nonrationality problem for generic cubic fourfolds

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Derived categories of quadric fibrations and intersections of quadrics

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Exceptional collection of vector bundles on \(V_{22}\) Fano threefolds

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Derived categories of Fano threefolds \(V_{12}\)

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Hyperplane sections and derived categories

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Homological projective duality

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Derived categories of Fano threefolds

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Derived Categories of Cubic Fourfolds

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Semiorthogonal decompositions in algebraic geometry

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Derived categories of cyclic covers and their branch divisors

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Exceptional collections on isotropic Grassmannians

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Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics

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The moduli space of cubic fourfolds via the period map

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The period map for cubic fourfolds

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Derived categories of surfaces isogenous to a higher product

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Uniqueness of enhancement for triangulated categories

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From exceptional collections to motivic decompositions via noncommutative motives

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On a characterization of a Jacobian variety

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Unramified elements in cycle modules

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Milnor's conjecture on quadratic forms and mod 2 motivic complexes

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Rational equivalence of O-cycles on surfaces

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Unirationality of Moduli Spaces of Special Cubic Fourfolds and K3 Surfaces

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Semi-orthogonal decomposability of the derived category of a curve

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An exceptional collection of vector bundles on the threefold \(V_ 5\)

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ASYMPTOTIC INVARIANTS OF SMOOTH MANIFOLDS

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Derived categories of coherent sheaves on Abelian varieties and equivalences between them

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Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities

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Combinatorial aspects of exceptional sequences on (rational) surfaces

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Unramified cohomology and rationality problems

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Invariants birationnels dans la suite spectrale de Bloch-Ogus

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Chow groups with coefficients

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Noether's problem over an algebraically closed field

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The Fourier Transform for Certain HyperKähler Fourfolds

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PRYM VARIETIES: THEORY AND APPLICATIONS

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Noncommutative Motives

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Kodaira dimension of moduli of special cubic fourfolds

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The homotopy theory of dg-categories and derived Morita theory

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Hypersurfaces that are not stably rational

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THE INTEGRAL COHOMOLOGY OF THE HILBERT SCHEME OF TWO POINTS

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Exceptional collections, and the Néron-Severi lattice for surfaces

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Abel-Jacobi map, integral Hodge classes and decomposition of the diagonal

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Bloch's conjecture for Catanese and Barlow surfaces

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Degree 4 unramified cohomology with finite coefficients and torsion codimension 3 cycles

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Théorème de Torelli pour les cubiques de \({\mathbb{P}}^ 5\). (Torelli theorem for the cubics of \({\mathbb{P}}^ 5)\)

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Some aspects of the Hodge conjecture

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Unirational threefolds with no universal codimension \(2\) cycle

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On the universal \(\mathrm{CH}_0\) group of cubic hypersurfaces

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Chow Rings, Decomposition of the Diagonal, and the Topology of Families

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Chow ring and gonality of general abelian varieties

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On Castelnuovo's criterion of rationality P\(_a\)=P\(_2\)=0 of an algebraic surface

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Sitelinks

Mathematics(1 entry)

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