Motivic realizations of singularity categories and vanishing cycles

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

zbMATH Keywords

vanishing cyclesalgebraic K-theorymotives\(\ell\)-adic sheavesLandau-Ginzburg modelnoncommutative motivesmatrix factorisationsnearby cyclesdg-categories of singularitiesmotivic homotopy theory Morel-Voevodskymotivic realisations

Mathematics Subject Classification ID

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

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