Character sheaves in characteristic $p$ have nilpotent singular support
Confluentes Mathematici, Tome 17 (2025), pp. 1-10.

We prove that character sheaves of a reductive group defined over any characteristic have nilpotent singular support, partially extending the work of [5, 16] to positive characteristic. We do this by introducing a category of tame perverse sheaves and studying its properties.

Publié le :
DOI : 10.5802/cml.97
Classification : 10X99, 14A12, 11L05
Keywords: isotriviality, log-selfishness, Gauß law

Kostas I. Psaromiligkos 1

1 Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France
Licence : CC-BY-NC-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Kostas I. Psaromiligkos. Character sheaves in characteristic $p$ have nilpotent singular support. Confluentes Mathematici, Tome 17 (2025), pp. 1-10. doi : 10.5802/cml.97. https://cml.centre-mersenne.org/articles/10.5802/cml.97/

[1] Pramod Achar Perverse Sheaves and Applications to Representation Theory, Mathematical Surveys and Monographs, 258, American Mathematical Society, 2021 | DOI | MR | Zbl

[2] Owen Barrett The singular support of an -adic sheaf, Tunis. J. Math., Volume 6 (2024) no. 4, pp. 703-734 | DOI | MR | Zbl

[3] Alexander Beilinson Constructible sheaves are holonomic, Sel. Math., New Ser., Volume 22 (2016) no. 4, pp. 1797-1819 | DOI | MR | Zbl

[4] Alexander Beilinson; Joseph Bernstein; Pierre Deligne Faisceaux pervers. Actes du colloque ‘Analyse et Topologie sur les Espaces Singuliers’. Partie I, Astérisque, 100, Société Mathématique de France, 1982 | Numdam | Zbl

[5] Victor Ginzburg Admissible modules on a symmetric space, Orbites unipotentes et représentations. III. Orbites et faisceaux pervers (Astérisque), Volume 173-174, Société Mathématique de France, 1989, pp. 199-255 | Zbl

[6] Alexander Grothendieck Séminaire de géométrie algébrique du Bois Marie 1960/61 (SGA 1), dirigé par Alexander Grothendieck. Augmenté de deux exposés de M. Raynaud. Revêtements étales et groupe fondamental. Exposés I à XIII, Lecture Notes in Mathematics, 224, Springer, 1971 | DOI | Zbl

[7] Katharina Hübner; Alexander Schmidt The tame site of a scheme, Invent. Math., Volume 223 (2021) no. 2, pp. 379-443 | DOI | MR | Zbl

[8] Masaki Kashiwara; Pierre Schapira Sheaves on Manifolds, Grundlehren der Mathematischen Wissenschaften, 292, Springer, 1990 | DOI | MR | Zbl

[9] Moritz Kerz; Alexander Schmidt On different notions of tameness in arithmetic geometry, Math. Ann., Volume 346 (2010) no. 3, pp. 641-668 | DOI | MR | Zbl

[10] George Lusztig Character sheaves. I, Adv. Math., Volume 56 (1985) no. 3, pp. 193-237 | DOI | Zbl

[11] George Lusztig Character sheaves. II, Adv. Math., Volume 57 (1985) no. 3, pp. 226-265 | DOI | Zbl

[12] George Lusztig Character sheaves. III, Adv. Math., Volume 57 (1985) no. 3, pp. 266-315 | DOI | Zbl

[13] George Lusztig Character sheaves. IV, Adv. Math., Volume 59 (1986) no. 1, pp. 1-63 | DOI | Zbl

[14] George Lusztig Character sheaves. V, Adv. Math., Volume 61 (1986) no. 2, pp. 103-155 | DOI | Zbl

[15] J. G. M. Mars; Tonny A. Springer Character sheaves, Orbites unipotentes et représentations III. Orbites et faisceaux pervers (Astérisque), Volume 173-174, Société Mathématique de France, 1989, pp. 111-198 | Numdam | MR | Zbl

[16] Ivan Mirković; Kari Vilonen Characteristic varieties of character sheaves, Invent. Math., Volume 93 (1988) no. 2, pp. 405-418 | DOI | MR | Zbl

[17] Takeshi Saito The characteristic cycle and the singular support of a constructible sheaf, Invent. Math., Volume 207 (2017) no. 2, pp. 597-695 Correction ibid 216(3):1005–1006, 2019 | DOI | MR | Zbl

[18] Tong Zhou Character Sheaves on Reductive Lie Algebras in Positive Characteristic (2024) | arXiv

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