2025/05/03 by Sam K. Miller, Miller, Sam K. · 2 citations
Mathematics · #16E40 #16T05 #18E30 #18F99 #18M05 #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #K-Theory and Homology (math.KT) #Mathematics and Applications #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2505.01899
openalex publication_date 2025/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two pertinent questions for any support theory of a monoidal triangulated category are whether it is functorial and if the tensor product property holds. To this end, we consider the complete prime spectrum of an essentially small monoidal triangulated category, which we show is universal among support data satisfying the tensor product property, even if it is empty. The complete prime spectrum is functorial and parametrizes radical thick tensor-ideals, a noncommutative analogue of Balmer's reconstruction theorem. We give criteria for when induced maps on complete prime spectra are injective or surjective, and determine the complete prime spectrum for crossed product categories. Finally, we determine the universal functorial support theory for monoidal triangulated categories coinciding with the Balmer spectrum on braided monoidal triangulated categories.