Betti Tate’s thesis and the trace of perverse schobers

Benjamin Gammage; Justin Hilburn

doi:10.5802/crmath.703

Article de recherche - Géométrie et Topologie, Théorie des représentations

Betti Tate’s thesis and the trace of perverse schobers
[La thèse de Tate dans le contexte de Betti et la trace des schobers pervers]

Benjamin Gammage ¹ ; Justin Hilburn ²

¹ Department of Mathematics, Harvard University, Cambridge, MA, USA
² Perimeter Institute, Waterloo, Ontario, Canada

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 169-181.

Résumé
Abstract

Nous proposons une conjecture sur la trace catégorique de la 2-catégorie des schobers pervers (qui modélisent conjecturalement la 2-catégorie de Fukaya-Fueter d’une variété symplectique holomorphe). En prouvant une version de la thèse de Tate dans le contexte de Betti, et en la combinant avec notre précédente équivalence de symétrie miroir 3D et le théorème de Ben-Zvi-Nadler-Preygel sur les traces spectrales, nous établissons notre conjecture dans le cas intéressant le plus simple.

We propose a conjecture on the categorical trace of the 2-category of perverse schobers (expected to model the Fukaya–Fueter 2-category of a holomorphic symplectic space). By proving a Betti geometric version of Tate’s thesis, and combining it with our previous 3d mirror symmetry equivalence and the Ben-Zvi–Nadler–Preygel result on spectral traces, we are able to establish our conjecture in the simplest interesting case.

Reçu le : 2024-09-10
Révisé le : 2024-10-23
Accepté le : 2024-11-12
Publié le : 2025-03-25

DOI : 10.5802/crmath.703

Affiliations des auteurs :

Benjamin Gammage ¹ ; Justin Hilburn ²

¹ Department of Mathematics, Harvard University, Cambridge, MA, USA
² Perimeter Institute, Waterloo, Ontario, Canada

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Benjamin Gammage and Justin Hilburn},
     title = {Betti {Tate{\textquoteright}s} thesis and the trace of perverse schobers},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {169--181},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     year = {2025},
     doi = {10.5802/crmath.703},
     language = {en},
}

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Benjamin Gammage; Justin Hilburn. Betti Tate’s thesis and the trace of perverse schobers. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 169-181. doi : 10.5802/crmath.703. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.703/

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