Microlocal perverse schobers and Radon transform

@misc{okitani2026microlocal,
  title = {{Microlocal perverse schobers and Radon transform}},
  author = {Yuji Okitani},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19692},
  eprint = {2609.19692},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19692},
}

TY  - UNPB
TI  - Microlocal perverse schobers and Radon transform
AU  - Yuji Okitani
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19692
UR  - https://arxiv.org/abs/2609.19692
AB  - Perverse schobers are a categorification of perverse sheaves, originally proposed by Kapranov and Schechtman. The purpose of this paper is to initiate a microlocal study of perverse schobers. We first categorify Perv(ℂ,R)/Loc(ℂ), the category of perverse sheaves on a complex line with singular points at R, modulo local systems. We use this to propose a general definition for microlocal perverse schobers supported on the open conormal to a germ of a hypersurface, and we conjecture that this is invariant under Radon transform. Here we make the key observation that while the analogous quotient of perverse schobers 2Perv(ℂ,R)/2Loc(ℂ) is a reasonable categorification, the resulting theory fails to be invariant under Radon transform. In fact, our proposed categorification can be recovered by correcting an instance of this failure in a universal manner. We prove Radon invariance when our hypersurface is the curve y^m=x^n in ℂ^2_x,y. Along the way, we explain how our theory relates to Fourier transforms of perverse schobers, periodic SODs, and spherical monads.
ER  -