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PreprintCC BY-NC-SA 4.0arXiv

Coleman Isomorphisms in Syntomic Cohomology and THH

  • Kush Singhal
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Abstract

This paper proves a generalisation of Coleman's isomorphism (between norm compatible cyclotomic units and a group of invertible power series) to various cohomology theories evaluated on proper regular p-adic formal schemes, for future applications to Iwasawa theory. This generalisation is an immediate consequence of a description, as a cyclotomic synthetic spectrum, of the limit over transfer maps as one goes up the cyclotomic tower of motivically filtered THH. This crucially uses a calculation of THH(ℤp[ζpn]) due to Devalapurkar--Raksit as well as a calculation of the free loop transfer due to Schlichtkrull. Along the way, we construct transfer maps for various cohomology theories along finite locally free regular maps, using some elements of ℙ1-stable motivic homotopy theory.

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Cite

BibTeXRIS
BibTeX
@misc{singhal2026coleman,
  title = {{Coleman Isomorphisms in Syntomic Cohomology and $\mathrmTHH$}},
  author = {Kush Singhal},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05252},
  eprint = {2609.05252},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05252},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Coleman Isomorphisms in Syntomic Cohomology and THH
AU  - Kush Singhal
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05252
UR  - https://arxiv.org/abs/2609.05252
AB  - This paper proves a generalisation of Coleman's isomorphism (between norm compatible cyclotomic units and a group of invertible power series) to various cohomology theories evaluated on proper regular p-adic formal schemes, for future applications to Iwasawa theory. This generalisation is an immediate consequence of a description, as a cyclotomic synthetic spectrum, of the limit over transfer maps as one goes up the cyclotomic tower of motivically filtered THH. This crucially uses a calculation of THH(ℤ_p[ζ_p^n]) due to Devalapurkar--Raksit as well as a calculation of the free loop transfer due to Schlichtkrull. Along the way, we construct transfer maps for various cohomology theories along finite locally free regular maps, using some elements of ℙ^1-stable motivic homotopy theory.
ER  -