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Relative Brauer groups and Kummer Sequence without characteristic constraint in fppf-topology

  • Sourayan Banerjee
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Abstract

Let f: X→ S be a faithful affine map. In this article we construct a group homomorphism θfppf: Br(f) ⟶ H1fppf (S, (f*𝒪X× / 𝒪S×)fppf), extending the formerly defined morphism over an étale site θet. In doing so, we eliminate the characteristic constraint previously found in the relative version of Kummer's exact sequence. Furthermore, given a finite subintegral extension of noetherian rings A ↪ B, we show that all the fppf cohomology groups, Hifppf(Spec(A),μfn); ∀ i≥ 0 vanish whenever n does not divide the characteristic of A.

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Cite

BibTeXRIS
BibTeX
@misc{banerjee2026relative,
  title = {{Relative Brauer groups and Kummer Sequence without characteristic constraint in $fppf$-topology}},
  author = {Sourayan Banerjee},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04760},
  eprint = {2609.04760},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04760},
}
RIS
TY  - UNPB
TI  - Relative Brauer groups and Kummer Sequence without characteristic constraint in fppf-topology
AU  - Sourayan Banerjee
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.04760
UR  - https://arxiv.org/abs/2609.04760
AB  - Let f: X→ S be a faithful affine map. In this article we construct a group homomorphism θ_fppf: Br(f) ⟶ H^1_fppf (S, (f_*𝒪_X^× / 𝒪_S^×)_fppf), extending the formerly defined morphism over an étale site θ_et. In doing so, we eliminate the characteristic constraint previously found in the relative version of Kummer's exact sequence. Furthermore, given a finite subintegral extension of noetherian rings A ↪ B, we show that all the fppf cohomology groups, H^i_fppf(Spec(A),μ^f_n); ∀ i≥ 0 vanish whenever n does not divide the characteristic of A.
ER  -