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Keller maps and holonomic D-modules
Abstract
Let kk be a field of characteristic p and R=kk[x1,…,xn]. Let D denote the ring of kk-linear differential operators on R. Let φ:R→ R be a kk-algebra endomorphism whose Jacobian is a unit in R. We show that there is a unique kk-algebra endomorphism Φ:D→ D such that Φ|R=φ and that the restriction of scalar via Φ preserves holonomicity. We also construct an example of a kk-algebra endomorphism of D that does not preserve holonomicity.
Related
BibTeX
@misc{zhang2026keller,
title = {{Keller maps and holonomic $D$-modules}},
author = {Wenliang Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10180},
eprint = {2609.10180},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10180},
}
RIS
TY - UNPB
TI - Keller maps and holonomic D-modules
AU - Wenliang Zhang
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10180
UR - https://arxiv.org/abs/2609.10180
AB - Let kk be a field of characteristic p and R=kk[x_1,…,x_n]. Let D denote the ring of kk-linear differential operators on R. Let φ:R→ R be a kk-algebra endomorphism whose Jacobian is a unit in R. We show that there is a unique kk-algebra endomorphism Φ:D→ D such that Φ|_R=φ and that the restriction of scalar via Φ preserves holonomicity. We also construct an example of a kk-algebra endomorphism of D that does not preserve holonomicity.
ER -