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Paper   IPM / M / 2302
School of Mathematics
  Title:   Depth formulas, restricted Tor-dimension under base change
1.  T. Sharif
2.  S. Yassemi
  Status:   Published
  Journal: Rocky Mountain J. Math.
  Vol.:  34
  Year:  2004
  Pages:   1131-1146
  Supported by:  IPM
Let R be a commutative Noetherian ring and let M and N be R-modules. It is shown that
{i|ToriR(M,N) ≠ 0}= sup
{depth R\frakpdepthR\frakpM\frakpdepthR\frakp N\frakp|\frakpSupp MSupp N}
provided that M has finite dimension. Assume that R is a complete local ring, M a finitely generated R-module, and, N an R-module of finite flat dimension. It is then proved that
{i|ExtRi(N,M) ≠ 0}=depthRdepth N.
TdRM= sup
{i ∈ \mathbbN0|ToriR(T,M) ≠ 0  for  some T  of  finite  flat  dimension}.
In addition, some results concerning TdR M under base change are given.

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