Mathematics – K-Theory and Homology
Scientific paper
2011-04-14
Mathematics
K-Theory and Homology
26 pages. Revised and final version. To appear in Advances in Mathematics
Scientific paper
In this article we initiate the study of the tensor triangular geometry of the categories Mot(k)_a and Mot(k)_l of non-commutative motives (over a base ring k). Since the full computation of the spectrum of Mot(k)_a and Mot(k)_l seems completely out of reach, we provide some information about the spectrum of certain subcategories. More precisely, we show that when k is a finite field (or its algebraic closure) the spectrum of the monogenic cores Core(k)_a and Core(k)_l (i.e. the thick triangulated subcategories generated by the tensor unit) is closely related to the Zariski spectrum of the integers. Moreover, we prove that if we slightly enlarge Core(k)_a to contain the non-commutative motive 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 the integers.
Dell'Ambrogio Ivo
Tabuada Goncalo
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