Feuilleter
no. 4
Shifted Contact Structures and Their Local Theory
Kadri İlker Berktav1
1 University of Zurich, Institute of Mathematics, Winterthurerstrasse 190 CH-8057 Zurich, Switzerland
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 4, pp. 1019-1057.

Dans cet article, nous définissons formellement des structures contacts k-décalées sur des champs (d’Artin) dérivés et étudions leurs propriétés locales dans le contexte de la géométrie algébrique dérivée. À cet égard, pour les 𝕂-schémas dérivés contacts k-décalés, nous développons un théorème de type Darboux et formulons la notion de symplectification.

In this paper, we formally define k-shifted contact structures on derived (Artin) stacks and study their local properties in the context of derived algebraic geometry. In this regard, for k-shifted contact derived 𝕂-schemes, we develop a Darboux-like theorem and formulate the notion of symplectification.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1795
Classification : 14A20, 14A30, 14F08
Keywords: derived algebraic geometry, shifted symplectic structures, contact geometry
Mots-clés : la géométrie algébrique dérivée, structures symplectiques décalées, géométrie contact

Kadri İlker Berktav 1

1 University of Zurich, Institute of Mathematics, Winterthurerstrasse 190 CH-8057 Zurich, Switzerland
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{AFST_2024_6_33_4_1019_0,
     author = {Kadri \.Ilker Berktav},
     title = {Shifted {Contact} {Structures} and {Their} {Local} {Theory}},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {1019--1057},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 33},
     number = {4},
     year = {2024},
     doi = {10.5802/afst.1795},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1795/}
}
TY  - JOUR
AU  - Kadri İlker Berktav
TI  - Shifted Contact Structures and Their Local Theory
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2024
SP  - 1019
EP  - 1057
VL  - 33
IS  - 4
PB  - Université Paul Sabatier, Toulouse
UR  - https://afst.centre-mersenne.org/articles/10.5802/afst.1795/
DO  - 10.5802/afst.1795
LA  - en
ID  - AFST_2024_6_33_4_1019_0
ER  - 
%0 Journal Article
%A Kadri İlker Berktav
%T Shifted Contact Structures and Their Local Theory
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2024
%P 1019-1057
%V 33
%N 4
%I Université Paul Sabatier, Toulouse
%U https://afst.centre-mersenne.org/articles/10.5802/afst.1795/
%R 10.5802/afst.1795
%G en
%F AFST_2024_6_33_4_1019_0
Kadri İlker Berktav. Shifted Contact Structures and Their Local Theory. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 4, pp. 1019-1057. doi : 10.5802/afst.1795. https://afst.centre-mersenne.org/articles/10.5802/afst.1795/

[1] Mathieu Anel The geometry of ambiguity: an introduction to the ideas of derived geometry, New spaces in mathematics—formal and conceptual reflections, Cambridge University Press, 2021, pp. 505-553 | DOI | MR | Zbl

[2] Vladimir I. Arnolʼd Mathematical Methods of Classical Mechanics, Nauka, 1989 | DOI

[3] Oren Ben-Bassat; Christopher Brav; Vittoria Bussi; Dominic Joyce A ‘Darboux theorem’ for shifted symplectic structures on derived Artin stacks, with applications, Geom. Topol., Volume 19 (2015) no. 3, pp. 1287-1359 | DOI | MR | Zbl

[4] Christopher Brav; Vittoria Bussi; Dominic Joyce A Darboux theorem for derived schemes with shifted symplectic structure, J. Am. Math. Soc., Volume 32 (2019) no. 2, pp. 399-443 | DOI | MR | Zbl

[5] Damien Calaque Shifted cotangent stacks are shifted symplectic, Ann. Fac. Sci. Toulouse, Math., Volume 28 (2019) no. 1, pp. 67-90 | DOI | Numdam | MR | Zbl

[6] Damien Calaque; Tony Pantev; Bertrand Toën; Michel Vaquié; Gabriele Vezzosi Shifted Poisson structures and deformation quantization, J. Topol., Volume 10 (2017) no. 2, pp. 483-584 | DOI | MR | Zbl

[7] Hansjörg Geiges An introduction to contact topology, Cambridge Studies in Advanced Mathematics, 109, Cambridge University Press, 2008 | DOI | MR

[8] Albin Grataloup Derived Symplectic Reduction and L-Equivariant Geometry (2023) | arXiv | DOI

[9] Dominic Joyce; Pavel Safronov A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes, Ann. Fac. Sci. Toulouse, Math., Volume 28 (2019), pp. 831-908 | DOI | Numdam | MR | Zbl

[10] Jacob Lurie Derived algebraic geometry, Ph. D. Thesis, Massachusetts Institute of Technology (2004)

[11] Jacob Lurie Higher algebra, 2017

[12] Tony Pantev; Bertrand Toën; Michel Vaquié; Gabriele Vezzosi Shifted symplectic structures, Publ. Math., Inst. Hautes Étud. Sci., Volume 117 (2013), pp. 271-328 | DOI | Numdam | MR | Zbl

[13] Pavel Safronov Shifted Poisson structures in representation theory (2019) (lecture notes)

[14] Ana C. Silva Lectures on Symplectic Geometry, Lecture Notes in Mathematics, 1764, Springer, 2008 | DOI | MR

[15] Bertrand Toën Derived algebraic geometry, EMS Surv. Math. Sci., Volume 1 (2014) no. 2, pp. 153-240 | DOI | MR | Zbl

[16] Bertrand Toën; Gabriele Vezzosi Homotopical algebraic geometry. II. Geometric stacks and applications, Mem. Am. Math. Soc., Volume 193 (2008) no. 902, p. x+224 | DOI | MR | Zbl

[17] Gabriele Vezzosi What is... a Derived Stack?, Notices Am. Math. Soc., Volume 58 (2011) no. 7, pp. 955-958 | MR | Zbl

Cité par Sources :