Mathematical Sciences Classification System

13Dxx - Homological methods
{For noncommutative rings, see 16Exx; for general categories, see 18Gxx}

  • 10
    13D02
    Syzygies, resolutions, complexes
  • 2
    13D03
    (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
  • 2
    13D05
    Homological dimension
  • 13D07
    Homological functors on modules (Tor, Ext, etc.)
  • 1
    13D09
    Derived categories
  • 3
    13D10
    Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 32Gxx]
  • 1
    13D15
    Grothendieck groups, $K$-theory [See also 14C35, 18F30, 19Axx, 19D50]
  • 13D22
    Homological conjectures (intersection theorems)
  • 13D25
    Complexes
  • 1
    13D30
    Torsion theory [See also 13C12, 18E40]
  • 4
    13D40
    Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
  • 6
    13D45
    Local cohomology [See also 14B15]
  • 13D99
    None of the above, but in this section

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