On a Consequence of the Order Ideal Conjecture

2013/05/08 by Sankar P. Dutta, Dutta, Sankar P.
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC

paper · pdf · doi:10.48550/arxiv.1305.1709

arxiv created 2013/05/08 · arxiv updated 2013/05/09

Abstract

Given a minimal set of generators \boldx of an ideal I of height d in a regular local ring (R, m, k) we prove several cases for which the map K_d(\boldx; R) ⊗ k → \Tor_d^R (R/I, k) is the 0-map. As a consequence of the order ideal conjecture we derive several cases for which K_d+i(\boldx; R) ⊗ k → \Tor_d+i^R (R/I, k) are 0-maps for i ≥ 0.

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