Monodromic Perverse Sheaves on Shifted Contact Stacks
Abstract
Applying the BBDJS minimal model to the derived symplectification of a −1-shifted contact derived Artin stack and descending algebraically along the structural free 𝔾m-action, we construct an ℓ-adic perverse sheaf on any oriented such stack, and use Verdier's specialization equivalence for monodromic sheaves to equip it with a tame twisted monodromy operator θ. We show that the local fundamental class of a Legendrian L satisfies θ∘ μL = (−1)vdim LμL, so that on Legendrians of odd virtual dimension, the class vanishes due to θ-invariance. Moreover, both parities occur already on the A1 chart while an odd Legendrian can carry a nonzero local class. We further formulate a contact analogue of Joyce's conjecture for a graded orientation, in which the orientation datum is twisted by the parity of the virtual dimension. Under the assumption of a monodromic refinement of the symplectic conjecture, we construct the categorified Legendrian 2-categories Lℱc(X) and LLeg0 via ℓ-adic pull-push functors. Finally, we show that the contact Behrend function is identically $1$, so that the associated Donaldson-Thomas invariant is the compactly supported étale Euler characteristic of the classical truncation, and that the higher traces of θ recover the singularity type that the first trace discards. As an application, we show that the symplectic invariant of a derived intersection of conic Lagrangians in a cotangent bundle vanishes identically, while the contact invariant computes the Euler characteristic of the projectivized intersection, with an explicit formula for conormal bundles.
Related
BibTeX
@misc{izbudak2026monodromic,
title = {{Monodromic Perverse Sheaves on Shifted Contact Stacks}},
author = {Efe İzbudak},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18796},
eprint = {2609.18796},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18796},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Monodromic Perverse Sheaves on Shifted Contact Stacks
AU - Efe İzbudak
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18796
UR - https://arxiv.org/abs/2609.18796
AB - Applying the BBDJS minimal model to the derived symplectification of a −1-shifted contact derived Artin stack and descending algebraically along the structural free 𝔾_m-action, we construct an ℓ-adic perverse sheaf on any oriented such stack, and use Verdier's specialization equivalence for monodromic sheaves to equip it with a tame twisted monodromy operator θ. We show that the local fundamental class of a Legendrian L satisfies θ∘ μ_L = (−1)^vdim Lμ_L, so that on Legendrians of odd virtual dimension, the class vanishes due to θ-invariance. Moreover, both parities occur already on the A_1 chart while an odd Legendrian can carry a nonzero local class. We further formulate a contact analogue of Joyce's conjecture for a graded orientation, in which the orientation datum is twisted by the parity of the virtual dimension. Under the assumption of a monodromic refinement of the symplectic conjecture, we construct the categorified Legendrian 2-categories Lℱ_c(X) and LLeg_0 via ℓ-adic pull-push functors. Finally, we show that the contact Behrend function is identically $1$, so that the associated Donaldson-Thomas invariant is the compactly supported étale Euler characteristic of the classical truncation, and that the higher traces of θ recover the singularity type that the first trace discards. As an application, we show that the symplectic invariant of a derived intersection of conic Lagrangians in a cotangent bundle vanishes identically, while the contact invariant computes the Euler characteristic of the projectivized intersection, with an explicit formula for conormal bundles.
ER -