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Intrinsic Restriction Traces and Toric Dynamics

  • Haoyang Liu
  • Tianle Liu
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Abstract

We prove Morita invariance of the Campbell--Lind--Malkiewich--Ponto--Zakharevich restriction-system trace after passage to perfect modules. It therefore defines an intrinsic integral restriction trace for an exact endofunctor of a small idempotent-complete stable ∞-category. On π0, the m-th ghost is the laced trace of the m-fold iterate, compatibly with Frobenius. For lattice-graded algebras, the ghost targets have twisted cocenters in degree zero; over the open parameter torus, this applies to the cyclic bimodule of Dinkins--Karpov--Krylov. For finite monomial endomorphisms of toric varieties, we construct motivic restriction classes whose ghosts are sums over cones fixed by the iterates. In one example, two classes have the same first ghost, while their second ghosts differ after rational Betti realization.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026intrinsic,
  title = {{Intrinsic Restriction Traces and Toric Dynamics}},
  author = {Haoyang Liu and Tianle Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08129},
  eprint = {2609.08129},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08129},
}
RIS
TY  - UNPB
TI  - Intrinsic Restriction Traces and Toric Dynamics
AU  - Haoyang Liu
AU  - Tianle Liu
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08129
UR  - https://arxiv.org/abs/2609.08129
AB  - We prove Morita invariance of the Campbell--Lind--Malkiewich--Ponto--Zakharevich restriction-system trace after passage to perfect modules. It therefore defines an intrinsic integral restriction trace for an exact endofunctor of a small idempotent-complete stable ∞-category. On π_0, the m-th ghost is the laced trace of the m-fold iterate, compatibly with Frobenius. For lattice-graded algebras, the ghost targets have twisted cocenters in degree zero; over the open parameter torus, this applies to the cyclic bimodule of Dinkins--Karpov--Krylov. For finite monomial endomorphisms of toric varieties, we construct motivic restriction classes whose ghosts are sums over cones fixed by the iterates. In one example, two classes have the same first ghost, while their second ghosts differ after rational Betti realization.
ER  -