2021/07/12 by Tony J. Puthenpurakal, Puthenpurakal, Tony J.
Mathematics · #13D02 #13D09 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 13C14 #Representation Theory (math.RT) #Secondary 13C60
paper · pdf · doi:10.48550/arxiv.2107.05237
openalex publication_date 2021/07/12 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Let (A,\mathfrakm) be a Gorenstein local ring and let CMS(A) be its stable category of maximal CM A-modules. Suppose CMS(A) ≅ CMS(B) as triangulated categories. Then we show (1) If A is a complete intersection of codimension c then so is B. (2) If A, B are Henselian and not hypersurfaces then dim A = dim B. (3) If A, B are Henselian and A is an isolated singularity then so is B. We also give some applications of our results. It should be remarked that if R,S are complete CM but not necessarily Gorenstein and if there is an triangle isomorphism between the singularity categories of R and S then it is possible that dim R - dim S is odd, see M.~Kalck; Adv. Math. 390 (2021), Paper No. 107913.