Brown--Adams representability for triangulated categories with locally coherent cohomology

2024/05/10 by George Ciprian Modoi, Modoi, George Ciprian
Computer Science · Decision Sciences · #18G35 #18G80 #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.2405.06475

openalex publication_date 2024/05/10 · openalex created_date 2024/05/14 · openalex updated_date 2026/07/28

Abstract

In this paper, we deal with two types of representability. The first is a variant of the Brown representability theorem in the spirit of Rouquier and Neeman. The second is a variant of the Brown-Adams representability. If A is a dg-algebra over a commutative noetherian ring R, such that A has coherent cohomology, it is shown that every cohomological (contravariant) functor M:D_perf(A)\toMod\textrm-R, also satisfying M(A[-n])\inmod\textrm-R, for all n∈ℤ is isomorphic to D(A)(-,X)|_D_perf(A), where X\inD(A) is such that Hⁿ(X) is coherent for all n∈ℤ.

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