arXiv subjects

Jean-Luc Portner

Publications and source records attributed to Jean-Luc Portner.

2 recordsLinked to original sources

arXiv2026

The motivic Lie algebra embeds into the cohomology of the general linear group

We show that the motivic Lie algebra of mixed Tate motives over $\mathbb{Z}$ embeds canonically into the unstable compactly-supported cohomology of locally symmetric spaces for $\mathrm{GL}_g(\mathbb{Z})$, and into the weight-zero compactly-supported cohomology of $\mathcal{A}_g$, the moduli space of principally polarized abelian varieties. Our construction passes through tropical geometry and graph complexes: compactly-supported analogues of the Borel classes pull back via the tropical Torelli map to canonical graph cocycles. The latter were recently identified with cocycles studied previously by Rossi and Willwacher. We combine their results with the theory of single-valued periods to conclude that the cocycles map to generators of the motivic Lie algebra. We also compute the canonical graph cocycles for all graphs with $\leq14$ edges.

math.AG↗

arXiv2026

Graph integrals, Feynman periods, and single-valued multiple zeta values

The Borel classes generating the stable cohomology of the general linear group can be represented by invariant differential forms. It is known that pulling these forms back along a tropical Torelli map yields canonical convergent integrals associated to graphs, which are closely connected to the cohomology of $\mathrm{GL}_n$ and of graph complexes. A natural question is what numbers these graph integrals are. We answer this for primitive canonical integrals by showing that they coincide with a family of complex position-space integrals arising in deformation quantisation. As a consequence, canonical integrals of graphs evaluate to single-valued multiple zeta values. We further deduce that every single-valued multiple zeta value occurs as a rational linear combination of Feynman periods of graphs with massless propagators. Finally, in the commutative graph complex, our result implies that the two associated cocycles agree.

math.QA↗