Exponentiation of motivic measures
Niranjan Ramachandran, Goncalo Tabuada
TL;DR
This paper investigates properties of motivic measures that can be exponentiated, demonstrating stability of Kapranov's zeta function's rationality under products and providing an elementary proof of a result by Totaro.
Contribution
It characterizes exponentiable motivic measures and applies these properties to prove stability of zeta function rationality and reprove Totaro's result.
Findings
Rationality of Kapranov's zeta function is stable under products
Elementary proof of Totaro's result
Properties of exponentiable motivic measures
Abstract
In this short note we establish some properties of all those motivic measures which can be exponentiated. As a first application, we show that the rationality of Kapranov's zeta function is stable under products. As a second application, we give an elementary proof of a result of Totaro.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Analytic Number Theory Research