English

Cohomology of $(\varphi, \tau)$-modules

Number Theory 2025-05-28 v3

Abstract

We construct cohomology theories for (φ,τ)(\varphi, \tau)-modules, and study their relation with cohomology of (φ,Γ)(\varphi, \Gamma)-modules, as well as Galois cohomology. Our method is axiomatic, and can treat the \'etale case, the overconvergent case, and the rigid-overconvergent case simultaneously. We use recent advances in locally analytic cohomology as a key ingredient.

Keywords

Cite

@article{arxiv.2402.02492,
  title  = {Cohomology of $(\varphi, \tau)$-modules},
  author = {Hui Gao and Luming Zhao},
  journal= {arXiv preprint arXiv:2402.02492},
  year   = {2025}
}

Comments

v3: final version. Changed section numberings and fixed some errors