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A Non Commutative Grauert Theorem and Fourier Mukai Duality for Generalized Complex Tori

  • Patrick Antweiler
  • Jonathan Block
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Abstract

We prove a generalization of Grauert's higher coherence theorem for a class of curved differential graded (non-commutative) Fréchet algebras. This allows us to extend the Fourier-Mukai calculus to derived categories arising in many new contexts. We then apply it and prove equivalence of derived categories of dual generalized complex tori using a non-commutative version of the Poincaré line bundle. This lays the foundation for categories of generalized complex branes on generalized complex tori. Examples include complex tori, symplectic tori as well as their non-commutative and B-field deformations.

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Cite

BibTeXRIS
BibTeX
@misc{antweiler2026commutative,
  title = {{A Non Commutative Grauert Theorem and Fourier Mukai Duality for Generalized Complex Tori}},
  author = {Patrick Antweiler and Jonathan Block},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01945},
  eprint = {2610.01945},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01945},
}
RIS
TY  - UNPB
TI  - A Non Commutative Grauert Theorem and Fourier Mukai Duality for Generalized Complex Tori
AU  - Patrick Antweiler
AU  - Jonathan Block
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01945
UR  - https://arxiv.org/abs/2610.01945
AB  - We prove a generalization of Grauert's higher coherence theorem for a class of curved differential graded (non-commutative) Fréchet algebras. This allows us to extend the Fourier-Mukai calculus to derived categories arising in many new contexts. We then apply it and prove equivalence of derived categories of dual generalized complex tori using a non-commutative version of the Poincaré line bundle. This lays the foundation for categories of generalized complex branes on generalized complex tori. Examples include complex tori, symplectic tori as well as their non-commutative and B-field deformations.
ER  -