TY - JOUR

T1 - Rigidity of Ext and Tor with Coefficients in Residue Fields of a Commutative Noetherian Ring

AU - Christensen, Lars Winther

AU - Iyengar, Srikanth B.

AU - Marley, Thomas

N1 - Funding Information:
Acknowledgements. We thank Peder Thompson for conversations that helped clarify the material in § 5. L.W.C. was partly supported by NSA grant H98230-14-0140 and Simons Foundation collaboration grant 428308. S.B.I. was partly supported by NSF grant DMS-1503044.
Publisher Copyright:
© 2018 Edinburgh Mathematical Society.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - Let be a prime ideal in a commutative noetherian ring R. It is proved that if an R-module M satisfies (k (), M) = 0 for some n R, where k() is the residue field at , then (k (), M) = 0 holds for all i n. Similar rigidity results concerning (k (), M) are proved, and applications to the theory of homological dimensions are explored.

AB - Let be a prime ideal in a commutative noetherian ring R. It is proved that if an R-module M satisfies (k (), M) = 0 for some n R, where k() is the residue field at , then (k (), M) = 0 holds for all i n. Similar rigidity results concerning (k (), M) are proved, and applications to the theory of homological dimensions are explored.

KW - Ext

KW - Tor

KW - flat dimension

KW - injective dimension

KW - rigidity

UR - http://www.scopus.com/inward/record.url?scp=85054733080&partnerID=8YFLogxK

U2 - 10.1017/S0013091518000081

DO - 10.1017/S0013091518000081

M3 - Article

AN - SCOPUS:85054733080

VL - 62

SP - 305

EP - 321

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 2

ER -