13Dxx


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Homological methods

{For noncommutative rings, see 16Exx; for general categories, see 18Gxx}

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