Remarques sur la cohomologie des groupes k\"ahl\'eriens nilpotents
Beno\^it Claudon (IF)

TL;DR
This paper demonstrates that the cohomology groups of (virtually) nilpotent K"ahler groups possess a natural mixed Hodge structure, and explores how this structure influences known examples of such groups.
Contribution
It establishes that cohomology groups of nilpotent K"ahler groups have a natural mixed Hodge structure, extending understanding of their geometric and algebraic properties.
Findings
Cohomology groups of nilpotent K"ahler groups carry a mixed Hodge structure.
Hopf morphisms are compatible with mixed Hodge structures.
Illustration with known examples of non-abelian nilpotent K"ahler groups.
Abstract
In this note, we show that the cohomology groups of (virtually) nilpotent K\"ahler groups are naturally endowed with a mixed Hodge structure. These structures make the Hopf morphisms into mixed Hodge structures morphisms. We illustrate this fact with the study of known examples of non-abelian nilpotent K\"ahler groups.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds
