Spectral sequences for Hochschild cohomology and graded centers of derived categories

• Frank Neumann ^[1] ; Markus Szymik ^[2]
  1. [1] University of Leicester

     University of Leicester

     GB.ENG.H4.31UC, Reino Unido

     
  2. [2] NTNU Norwegian University of Science and Technology
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 3, 2017, págs. 1997-2018
• Idioma: inglés
• DOI: 10.1007/s00029-017-0331-9
• Enlaces
  • Texto completo (pdf)
• Resumen

  • The Hochschild cohomology of a differential graded algebra, or a differential graded category, admits a natural map to the graded center of its homology category: the characteristic homomorphism. We interpret it as an edge homomorphism in a spectral sequence. This gives a conceptual explanation of the failure of the characteristic homomorphism to be injective or surjective, in general. To illustrate this, we discuss modules over the dual numbers, coherent sheaves over algebraic curves, as well as examples related to free loop spaces and string topology.