00 7 on the Multiplicities of a Motive
نویسنده
چکیده
We introduce the notion of multiplicities for an object M in a semi-simple rigid tensor category A, as a collection of central scalars which relate the categorical trace with the ring-theoretic trace. Multiplicities turn out to be rational integers in important cases, most notably when A is of " homological origin ". We show that this integrality condition has simple consequences, like the rationality and a functional equation for the zeta function of an (invertible) endomorphism. An example is the category of pure motives modulo numerical equivalence with rational coefficients over a field k; if k is finite and M is of abelian type, its multiplicities are all equal to ±1.
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تاریخ انتشار 2007