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PreprintCC BY 4.0arXiv

Integral trace duality and the Witt filtration on Lubin--Tate space

  • Andrea Taccani
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Abstract

Let 𝒪 be the Lubin--Tate deformation ring of a one-dimensional commutative formal group of finite height n≥1 over a perfect field k of characteristic p. We identify Rezk's Witt filtration {Id} with the divisibility filtration of integral trace pairings on subgroup algebras of fixed source lifts. This gives the geometric recursion Id+1=pId+Jd,z (d≥0), where Jd,z defines the targets of order-pd quotient isogenies from a W(k)-valued lift z of the closed point. The corrected ideal is independent of z. We also compute the cokernel of the universal source trace pairing over 𝒪: it is ⨁j=1d(𝒪/pj)rj−rj−1, where rj counts order-pj subgroups of (Qp/Zp)n. The same duality extends the generic trace along two-step isogeny flags to an integral surjection, even when the flag-forgetting map is not flat. This computes composition in the subring of weighted trace operations. Applications include sharp projector denominators and congruence fibre products for full-torsion loci.

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Cite

BibTeXRIS
BibTeX
@misc{taccani2026integral,
  title = {{Integral trace duality and the Witt filtration on Lubin--Tate space}},
  author = {Andrea Taccani},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18246},
  eprint = {2610.18246},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18246},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Integral trace duality and the Witt filtration on Lubin--Tate space
AU  - Andrea Taccani
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.18246
UR  - https://arxiv.org/abs/2610.18246
AB  - Let 𝒪 be the Lubin--Tate deformation ring of a one-dimensional commutative formal group of finite height n≥1 over a perfect field k of characteristic p. We identify Rezk's Witt filtration {I_d} with the divisibility filtration of integral trace pairings on subgroup algebras of fixed source lifts. This gives the geometric recursion I_d+1=pI_d+J_d,z (d≥0), where J_d,z defines the targets of order-p^d quotient isogenies from a W(k)-valued lift z of the closed point. The corrected ideal is independent of z. We also compute the cokernel of the universal source trace pairing over 𝒪: it is ⨁_j=1^d(𝒪/p^j)^r_j−r_j−1, where r_j counts order-p^j subgroups of (Q_p/Z_p)^n. The same duality extends the generic trace along two-step isogeny flags to an integral surjection, even when the flag-forgetting map is not flat. This computes composition in the subring of weighted trace operations. Applications include sharp projector denominators and congruence fibre products for full-torsion loci.
ER  -