Correspondences, Motifs and Monoidal Transformations

A note on functional equations for zeta functions with values in Chow motives

“…n and satisfies .13 and the decomposition of the motive of a blow-up as e.g., in [19], Section 9, shows that the property of having a rational zeta function satisfying a functional equation is closed under blow-ups along smooth centers satisfying a functional equation.…”

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“…By [10], the direct image i m p is the composition The localization exact sequence and the homotopy invariance then yield isomorphisms…”

Lefschetz and Hirzebruch–Riemann–Roch formulas via noncommutative motives

“…Given a field k, let Chow(k) Q be the Q-linear category of Chow motives; see [1,Chapter 4], [4,Chapter 16] or [12] for instance). This category is defined as the idempotent completion of the category whose objects are the pairs (X, m), with X a smooth and proper k-scheme, and whose morphisms are given by…”