We study (compactly supported) cohomology of character stacks of punctured Riemann surface with prescribed semisimple local monodromies at punctures. In the case of generic local monodromies, the cohomology of these character stacks has been studied in [23, 39]. In this paper we extend the results and conjectures of [23] to the non-generic case. In particular we compute the E-series and give a conjectural formula for the mixed Poincaré series. We prove our conjecture in the case of the projective line with punctures.
On étudie la cohomologie (à support compact) des champs de caractères pour les surfaces de Riemann épointées avec monodromies locales semi-simples fixées. Dans le cas de monodromies locales génériques, la cohomologie de ces champs de caractères a été étudiée dans [23, 39]. Dans cet article, on étend les résultats et la conjecture de [23] au cas non générique. En particulier, on calcule la E-série et on donne une formule conjecturale pour la série mixte de Poincaré. On démontre cette conjecture dans le cas de la droite projective privée de points.
Accepted:
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Keywords: Character varieties, compactly supported cohomology, moduli stacks
Mot clés : Variétés de caractères, cohomologie à support compact, champs de modules
Tommaso Scognamiglio 1
@article{JEP_2024__11__1287_0, author = {Tommaso Scognamiglio}, title = {Cohomology of non-generic character stacks}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {1287--1371}, publisher = {\'Ecole polytechnique}, volume = {11}, year = {2024}, doi = {10.5802/jep.278}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.278/} }
TY - JOUR AU - Tommaso Scognamiglio TI - Cohomology of non-generic character stacks JO - Journal de l’École polytechnique — Mathématiques PY - 2024 SP - 1287 EP - 1371 VL - 11 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.278/ DO - 10.5802/jep.278 LA - en ID - JEP_2024__11__1287_0 ER -
%0 Journal Article %A Tommaso Scognamiglio %T Cohomology of non-generic character stacks %J Journal de l’École polytechnique — Mathématiques %D 2024 %P 1287-1371 %V 11 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.278/ %R 10.5802/jep.278 %G en %F JEP_2024__11__1287_0
Tommaso Scognamiglio. Cohomology of non-generic character stacks. Journal de l’École polytechnique — Mathématiques, Volume 11 (2024), pp. 1287-1371. doi : 10.5802/jep.278. https://jep.centre-mersenne.org/articles/10.5802/jep.278/
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