On the pre-lambda ring structure on the Grothendieck ring of stacks and the power structures over it

TL;DR

This paper extends the pre-lambda and power structures from the Grothendieck ring of varieties to stacks, exploring their properties and providing explicit formulas for the Kapranov zeta function for certain stacks.

Contribution

It introduces a generalized pre-lambda structure on the Grothendieck ring of stacks and analyzes its properties and applications.

Findings

Extended pre-lambda structure to stacks

Derived explicit formulas for Kapranov zeta functions

Analyzed properties of the generalized structures

Abstract

In this note we discuss a generalization ("extension") of the pre-lambda structure on the Grothendieck ring of quasi-projective varieties and of the corresponding power structure over it to the Grothendieck ring of stacks, discuss some of their properties and give some explicit formulae for the Kapranov zeta function for some stacks.