Filtered derived categories of curved deformations

2024/02/13 by Lehmann, Alessandro, Lowen, Wendy
#13D10 #16E45 #18G25 (Secondary) #18G80 (Primary) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2402.08660

Abstract

We propose a solution to the "curvature problem" from arXiv:1505.03698 and arXiv:0905.3845 for infinitesimal deformations. Let k be a field, A a dg algebra over k and A_n = A[t]/(tⁿ⁺¹) a cdg algebra over R_n = k[t]/(tⁿ⁺¹), n ≥ 0, with reduction A_n/tA_n = A. We define the n-derived category Dⁿ(A_n) as the quotient of the homotopy category by the modules for which all quotients appearing in the associated graded object are acyclic. We prove this to be a compactly generated triangulated category with a semiorthogonal decomposition by n + 1 copies of D(A), in which Positselski's semiderived category embeds admissibly.

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