Towards a geometrisation of Deligne cohomology
Marco Artusa
CIRM-I2M
https://martusa.perso.math.cnrs.fr/
Date(s) : 05/05/2026 iCal
14h00 - 15h00
Deligne cohomology of a complex manifold Y is a hybrid object: it mixes Betti cohomology with the Hodge filtration on de Rham cohomology, producing a complex of locally compact abelian groups. Despite its central role in regulators and special-value conjectures, it lacks a geometric framework that treats the archimedean structure of de Rham cohomology and the discrete structure of Betti cohomology at the same time.
In this talk, we construct an analytic stack \mathcal{X} (in the sense of Clausen-Scholze) that serves as a universal base for such objects. Quasi-coherent sheaves on \mathcal{X} combine archimedean (liquid) modules and non-archimedean (solid) modules. In particular, Deligne cohomology groups appear as quasi-coherent sheaves on \mathcal{X}.
If time permits, we present a strategy to associate, to any complex analytic manifold Y, an analytic stack Y^{Del} over \mathcal{X}, whose relative cohomology should recover Deligne cohomology. This is a work in progress.
Emplacement
I2M Luminy - TPR2, Salle de Séminaire 304-306 (3ème étage)
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