Motivic stack inertia for modui spaces of curves, variation of periods and multiple zeta values in genus 0 and 1.

Principal Investigator

Dr. Benjamin Collas (Bayreuth)  

Project description

The goal of this project is to lead a study of the stack arithmetic properties of the moduli spaces of curves from the viewpoint of homotopical methods. The arithmetic of stack inertia has shown to share some strong analogy with the Deligne-Mumford divisorial inertia, the latter being a key component of the theory of Mixed Tate Motives and their periods. We will more precisely develop our approach in the context of the Morel-Voevodsky unstable motivic homotopy category. The étale topological type realisation functor here offers a link to recent progresses of the field in profinite Galois representation.

The moduli stack of curves presenting a computable example of Deligne-Mumford stacks, we will give a specific attention to the cases of genus zero and one curves. Through the Betti-de Rham realisation, a new type of periods should then appear that we plan to compare with the classical and elliptical multiple zeta values of genus zero and one respectively.

Related publications

Preprints

B. Collas, S. Maugeais, Hurwitz Stacks of Groups Extensions and Irreducibility. arxiv:1803.06212.

B. Collas, M. Dettweiler, S. Reiter, Monodromy of elliptic curve convolution and $G_2$-motives of Beauville-Katz type Available at arXiv:1803.05883

B. Collas, S. Maugeais, On Galois action on stack inertia of moduli spaces of curves. Available at arXiv:1412.4644.