Indecomposability of derived categories for arbitrary schemes

• López Martín, Ana Cristina ^[1] ; Sancho de Salas, Fernando ^[1]
  1. [1] Universidad de Salamanca

     Universidad de Salamanca

     Salamanca, España

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 3, 2024, págs. 639-658
• Idioma: inglés
• DOI: 10.1007/s13348-023-00404-w
• Texto completo no disponible (Saber más ...)
• Dialnet Métricas: 1 Cita
• Resumen

  • We extend the criterion of Kawatani and Okawa for indecomposability of the derived category of a smooth projective variety to arbitrary schemes. For relative schemes, we also give a criterion for the nonexistence of semiorthogonal decompositions that are linear over the base. These criteria are based on the base loci of the global or relative dualizing complexes.

• Referencias bibliográficas
  • Bondal, A. I., Kapranov, M. M.: Representable functors, Serre functors, and reconstructions. Izv. Akad. Nauk SSSR Ser. Mat. 53, 1183–1205...
  • Catanese, F.: Pluricanonical–Gorenstein-curves. In: Enumerative Geometry and Classical Algebraic Geometry (1982) (Nice,: vol. 24 of Progr....
  • Catanese, F., Franciosi, M., Hulek, K., Reid, M.: Embeddings of curves and surfaces. Nagoya Math. J. 154, 185–220 (1999)
  • Caucci, F.: Paracanonical base locus, Albanese morphism and semiorthogonal indecomposability of derived categories (2022). arXiv:2110.06795v2
  • Cossec, F. R., Dolgachev, I.: Enriques surfaces. I. In: Progress in Mathematics, Vol. 76, pp. x+397. Birkhäuser Boston Inc., Boston, MA...
  • Elagin, A., Lunts, V.: Regular subcategories in bounded derived categories of affine schemes. Sbornik Math. 209(12), 1756–1782 (2018)
  • Hernández Ruipérez, D., López Martín, A.C., de Salas, F.S.: Relative integral functors for singular fibrations and singular partners. J. Eur....
  • Kawatani, K., Okawa, S.: Nonexistence of semiorthogonal decompositions and sections of the canonical bundle (2018). arXiv:1508.00682v2
  • Kodaira, K.: On compact analytic surfaces. II, III. Ann. Math. 77(2), 563–626 (1963)
  • Kuznetsov, A.: Hyperplane sections and derived categories. Izv. Ross. Akad. Nauk Ser. Mat. 70(3), 23–128 (2006); translation in Izv. Math....
  • Kuznetsov, A.: Semiorthogonal decompositions in algebraic geometry. In: Proceedings of the International Congress of Mathematicians—Seoul...
  • Kuznetsov, A.: Semiorthogonal decompositions in families (2021). arXiv:2111.00527
  • Kuznetsov, A., Shinder, E.: Homologically finite-dimensional objects in triangulated categories (2022). arXiv:2211.09411
  • Kuznetsov, A., Shinder, E.: Categorical absorptions of singularities and degenerations (2022). arXiv:2207.06477
  • Lin, X.: On existence of semiorthogonal decompositions in algebraic geometry (2021). arXiv:2107.09564
  • Lipman, J.: Notes on derived functors and Grothendieck duality. In: Foundations of Grothendieck duality for Diagrams of Schemes, Lecture Notes...
  • Neeman, A.: The Grothendieck duality theorem via Bousfield’s techniques and Brown representability. J. Am. Math. Soc. 9(1), 205–236 (1996)
  • Okawa, S.: Semi-orthogonal decomposability of the derived category of a curve. Adv. Math. 228, 2869–2873 (2011)
  • Okawa, S.: Semiorthogonal indecomposability of minimal irregular surfaces (2023). arXiv:2304.14048v1
  • Orlov, D.O.: Triangulated categories of singularities, and equivalences between Landau–Ginzburg models. Mat. Sb. 197, 117–132 (2006)
  • Pirozhkov, D.: Stably semiorthogonally indecomposable varieties (2023). arXiv:2011.12743v3
  • Ran, Z.: Canonical systems and their limits on stable curves. J. Algebra 399, 634–656 (2014)
  • Sancho de Salas, F.: Koszul complexes and fully faithful integral functors. Bull. Lond. Math. Soc. 41, 1085–1094 (2009)
  • Spence, D.: A note on semiorthogonal indecomposability of some Cohen–Macaulay varieties. J. Pure Appl. Algebra 226, 107076 (2022)