Formal Laurent series rings and the Hermite ring conjecture

2022/04/13 by Daniel Schäppi, Schäppi, Daniel
Mathematics · #13C10 #19A13 #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AC #math.KT #msc:13C10 #msc:19A13

paper · pdf · doi:10.48550/arxiv.2204.06303

20 pages

arxiv created 2022/04/13 · arxiv updated 2022/04/14

Abstract

We study the question if projective modules over formal Laurent series rings are extended. We relate this question to the Bass-Quillen conjecture for commutative regular local rings and to the Hermite ring conjecture for all commutative local rings. Using our result about projective modules over formal Laurent series rings, we prove a reduction step for the Hermite ring conjecture. We show that the Hermite ring conjecture holds for all commutative local rings if and only if it holds for complete intersection rings which are also unique factorization domains.

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