Tensor triangular geometry of non-commutative motives

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Abstract

In this article we initiate the study of the tensor triangular geom- etry of the category Motk of non-commutative motives (over a base ring k). Since the full computation of the spectrum of Motk seems completely out of reach, we provide some information about the spectrum of certain subcat- egories of Motk. More precisely, we show that when k is a finite field (or its algebraic closure) the spectrum of the bootstrap subcategory of Motk is closely related to the Zariski spectrum of Z. Moreover, we prove that if we slightly enlarge the bootstrap category to contain the non-commutative mo- tive associated to the ring of polynomials k[t], and assume that k is a field of characteristic zero, then the corresponding spectrum is richer than the Zariski spectrum of Z.
Original languageUnknown
Pages (from-to)1329-1357
JournalAdvances In Mathematics
Volume229
Issue number2
DOIs
Publication statusPublished - 1 Jan 2012

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