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Colored Khovanov homology theories at prime roots of unity

Abstract

We equip Khovanov's colored gl(2)-homology groups with a degree-2 derivation. Over a field of characteristic p>2, the derivation specializes to a p-nilpotent differential, which leads to a categorification of colored gl(2)-homology at a 2pth root of unity.

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BibTeX
@misc{qi2026colored,
  title = {{Colored Khovanov homology theories at prime roots of unity}},
  author = {You Qi and Louis-Hadrien Robert and Joshua Sussan and Emmanuel Wagner},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01122},
  eprint = {2610.01122},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01122},
}
RIS
TY  - UNPB
TI  - Colored Khovanov homology theories at prime roots of unity
AU  - You Qi
AU  - Louis-Hadrien Robert
AU  - Joshua Sussan
AU  - Emmanuel Wagner
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01122
UR  - https://arxiv.org/abs/2610.01122
AB  - We equip Khovanov's colored gl(2)-homology groups with a degree-2 derivation. Over a field of characteristic p>2, the derivation specializes to a p-nilpotent differential, which leads to a categorification of colored gl(2)-homology at a 2pth root of unity.
ER  -