Geometric Phantom Categories
arXiv:1209.6183 · doi:10.1007/s10240-013-0050-5
Abstract
In this paper we give a construction of phantom categories, i.e. admissible triangulated subcategories in bounded derived categories of coherent sheaves on smooth projective varieties that have trivial Hochschild homology and trivial Grothendieck group. We also prove that these phantom categories are phantoms in a stronger sense, namely, they have trivial K-motives and, hence, all their higher K-groups are trivial too.
LaTeX, 18 pages
References in corpus (7)
- Hochschild homology and semiorthogonal decompositions
- Determinantal Barlow surfaces and phantom categories
- On the derived category of the classical Godeaux surface
- Derived categories of Burniat surfaces and exceptional collections
- Exceptional collections of line bundles on the Beauville surface
- Height of exceptional collections and Hochschild cohomology of quasiphantom categories
- Smoothness of equivariant derived categories
Cited by in corpus (22)
- Determinantal Barlow surfaces and phantom categories
- Derived categories of Burniat surfaces and exceptional collections
- Exceptional collections, and the Neron-Severi lattice for surfaces
- On the Jordan-Hölder property for geometric derived categories
- Finite-dimensional differential graded algebras and their geometric realizations
- Helix Structures in Quantum Cohomology of Fano Varieties
- Simplifying Weinstein Morse functions
- Cycles, derived categories, and rationality
- Derived noncommutative schemes, geometric realizations, and finite dimensional algebras
- A Phantom on a Rational Surface
- Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks
- Quasiphantom categories on a family of surfaces isogenous to a higher product
- Embeddings of algebras in derived categories of surfaces
- The integral cohomology of the Hilbert scheme of points on a surface
- Hodge numbers and Hodge structures for Calabi-Yau categories of dimension three
- Fullness of exceptional collections via stability conditions -- A case study: the quadric threefold
- Fano visitors, Fano dimension and orbifold Fano hosts
- Exceptional collection of objects on some fake projective planes
- Weil transfer of noncommutative motives
- Thick subcategories on weighted projective curves and nilpotent representations of quivers
- Note on Applications of Toric Systems on Surfaces
- Torsion birational motives of surfaces and unramified cohomology