Motivic realizations of singularity categories and vanishing cycles
From MaRDI portal
Publication:4559775
DOI10.5802/jep.81zbMath1423.14151arXiv1607.03012OpenAlexW2964174602MaRDI QIDQ4559775
Marco Robalo, Bertrand Toën, Anthony Blanc, Gabriele Vezzosi
Publication date: 4 December 2018
Published in: Journal de l’École polytechnique — Mathématiques (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1607.03012
vanishing cyclesalgebraic K-theorymotives\(\ell\)-adic sheavesLandau-Ginzburg modelnoncommutative motivesmatrix factorisationsnearby cyclesdg-categories of singularitiesmotivic homotopy theory Morel-Voevodskymotivic realisations
Noncommutative algebraic geometry (14A22) Rings arising from noncommutative algebraic geometry (16S38) Deformations of complex singularities; vanishing cycles (32S30) (K)-theory of schemes (19E08) Motivic cohomology; motivic homotopy theory (14F42)
Related Items
Singular Hochschild cohomology via the singularity category ⋮ Singularity categories via the derived quotient ⋮ Trace and Künneth formulas for singularity categories and applications ⋮ A physical origin for singular support conditions in geometric Langlands theory ⋮ On some (co)homological invariants of coherent matrix factorizations ⋮ The dg Leavitt algebra, singular Yoneda category and singularity category ⋮ Equivariant Hodge theory and noncommutative geometry ⋮ NOTES ON VANISHING CYCLES AND APPLICATIONS ⋮ The \(\ell \)-adic trace formula for dg-categories and Bloch's conductor conjecture ⋮ On the structure of dg categories of relative singularities ⋮ Motivic and \(\ell\)-adic realizations of the category of singularities of the zero locus of a global section of a vector bundle ⋮ Corrections to: ``Singular Hochschild cohomology via the singularity category ⋮ Cohomological methods in intersection theory
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Curved \(A_\infty\) algebras and Landau-Ginzburg models
- The closed state space of affine Landau-Ginzburg B-models
- Nearby motives and motivic nearby cycles
- Matrix factorizations for nonaffine LG-models
- Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
- \(K\)-theory and the bridge from motives to noncommutative motives
- Motivic vanishing cycles as a motivic measure
- Compact generators in categories of matrix factorizations
- Affine representability results in \(\mathbb A^1\)-homotopy theory. II: Principal bundles and homogeneous spaces
- On the motivic spectra representing algebraic cobordism and algebraic \(K\)-theory
- Higher \(K\)-theory via universal invariants
- Über die lokale Zetafunktion von Shimuravarietaeten. Monodromiefiltration und verschwindende Zyklen in ungleicher Charakteristik
- Cohomologie étale. Seminaire de géométrie algébrique du Bois-Marie SGA 4 1/2 par P. Deligne, avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier
- DG quotients of DG categories.
- Matrix factorizations over projective schemes
- A Quillen model structure on the category of dg categories
- On the conductor formula of Bloch
- Homology of schemes
- Descent by blow-ups for homotopy invariant \(K\)-theory
- Coherent analogues of matrix factorizations and relative singularity categories
- Singular support of coherent sheaves and the geometric Langlands conjecture
- Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
- Étale motives
- Symmetric monoidal structure on non-commutative motives
- Integral transforms and Drinfeld centers in derived algebraic geometry
- On exact -categories and the Theorem of the Heart
- Note sur les opérations de Grothendieck et la réalisation de Betti
- Algebraic K -theory, A 1 -homotopy and Riemann-Roch theorems
- Higher algebraic K-theory: I
- G\'eom\'etrie non-commutative, formule des traces et conducteur de Bloch
- Non-connective K-theory via universal invariants
- Cyclic Homology of Categories of Matrix Factorizations
- Kontsevich's conjecture on an algebraic formula for vanishing cycles of local systems
- Non-commutative Hodge structures: Towards matching categorical and geometric examples
- Moduli of objects in dg-categories
- La réalisation étale et les opérations de Grothendieck
- Higher Topos Theory (AM-170)
- \(\mathbb{A}^1\)-homotopy theory of schemes
