A Derived Legendrian Category for Shifted Contact Stacks
Abstract
For every integer s and every n ≥ 1, we construct a symmetric monoidal (∞,n)-category Legns whose objects are s-shifted contact derived Artin stacks and whose i-morphisms are i-fold Legendrian correspondences. The construction is based on the fact that an s-shifted contact structure on a derived Artin stack X is an s-shifted symplectic structure on X relative to B𝔾m, twisted by the weight-one line bundle, and that Legendrian structures are the corresponding relative Lagrangian structures. This lets us obtain the (∞,n)-categories Legns as twisted forms over B𝔾m of the (∞,n)-categories of iterated Lagrangian correspondences of Calaque, Haugseng and Scheimbauer, with the fiber product over B𝔾m as tensor product. For an s-shifted contact stack X, we then obtain the derived Legendrian category ℱc(X). Its objects are Legendrian morphisms into X, and its mapping categories are categories of Legendrians in derived Legendrian intersections, which carry (s−1)-shifted contact structures. The AKSZ construction gives oriented extended topological field theories with values in Legns, as well as shifted contact structures on the quotient mapping stacks [Map(Y,X̃)/𝔾m]. Our definitions of contact and Legendrian structures agree with those of Berktav where both are defined, for every shift.
Related
- Non-unital monoidal category of contact manifolds and Legendrian correspondence
- Monodromic Perverse Sheaves on Shifted Contact Stacks
- Degenerations of shifted symplectic moduli stacks of sheaves
- Degeneration of (-1)-shifted symplectic stacks and categorification of Donaldson-Thomas invariants
- Category 𝒪 for truncated shifted Yangians and the bi-infinite Bott-Samelson variety
BibTeX
@misc{izbudak2026derived,
title = {{A Derived Legendrian Category for Shifted Contact Stacks}},
author = {Efe İzbudak and Kadri İlker Berktav},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.13792},
eprint = {2605.13792},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.13792},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - A Derived Legendrian Category for Shifted Contact Stacks
AU - Efe İzbudak
AU - Kadri İlker Berktav
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2605.13792
UR - https://arxiv.org/abs/2605.13792
AB - For every integer s and every n ≥ 1, we construct a symmetric monoidal (∞,n)-category Leg_n^s whose objects are s-shifted contact derived Artin stacks and whose i-morphisms are i-fold Legendrian correspondences. The construction is based on the fact that an s-shifted contact structure on a derived Artin stack X is an s-shifted symplectic structure on X relative to B𝔾_m, twisted by the weight-one line bundle, and that Legendrian structures are the corresponding relative Lagrangian structures. This lets us obtain the (∞,n)-categories Leg_n^s as twisted forms over B𝔾_m of the (∞,n)-categories of iterated Lagrangian correspondences of Calaque, Haugseng and Scheimbauer, with the fiber product over B𝔾_m as tensor product. For an s-shifted contact stack X, we then obtain the derived Legendrian category ℱ_c(X). Its objects are Legendrian morphisms into X, and its mapping categories are categories of Legendrians in derived Legendrian intersections, which carry (s−1)-shifted contact structures. The AKSZ construction gives oriented extended topological field theories with values in Leg_n^s, as well as shifted contact structures on the quotient mapping stacks [Map(Y,X̃)/𝔾_m]. Our definitions of contact and Legendrian structures agree with those of Berktav where both are defined, for every shift.
ER -