A cohomological study of local rings of embedding codepth 3

AbstractThe generating series of the Bass numbers μRi=rankkExtRi(k,R) of local rings R with residue field k are computed in closed rational form, in case the embedding dimension e of R and its depth d satisfy e−d≤3. For each such R it is proved that there is a real number γ>1, such that μRd+i≥γμRd+i−1 holds for all i≥0, except for i=2 in two explicitly described cases, where μRd+2=μRd+1=2. New restrictions are obtained on the multiplicative structures of minimal free resolutions of length 3 over regular local rings