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Tropicalization and Polyhedral Completions of Weyl Algebras
Abstract
We construct weighted and polyhedral completions of the Weyl algebra over a complete nonarchimedean field and organize them into a structure sheaf on a polyhedral G-site. For discretely valued fields, we prove two-sided flatness for Γ-rational polyhedral completions, yielding exact base change for finitely generated D-modules. For compact integral polyhedra, we also construct finite-type integral models whose special fibers are toric face rings and describe the reduction of Gauss points in terms of toric strata.
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BibTeX
@misc{hsiao2026tropicalization,
title = {{Tropicalization and Polyhedral Completions of Weyl Algebras}},
author = {Jen-Chieh Hsiao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41578},
eprint = {2610.41578},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41578},
}
RIS
TY - UNPB
TI - Tropicalization and Polyhedral Completions of Weyl Algebras
AU - Jen-Chieh Hsiao
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41578
UR - https://arxiv.org/abs/2610.41578
AB - We construct weighted and polyhedral completions of the Weyl algebra over a complete nonarchimedean field and organize them into a structure sheaf on a polyhedral G-site. For discretely valued fields, we prove two-sided flatness for Γ-rational polyhedral completions, yielding exact base change for finitely generated D-modules. For compact integral polyhedra, we also construct finite-type integral models whose special fibers are toric face rings and describe the reduction of Gauss points in terms of toric strata.
ER -