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Hartl's dictionary and a transcendence characterization of equicharacteristic local shtukas with complex multiplication

  • Minhua Cheng
  • Sean Howe
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Abstract

We update Hartl's dictionary between p-adic Hodge theory and its equicharacteristic analog to include aspects related to the Hodge--Tate filtration in p-adic Hodge theory and its equicharacteristic analog, the Hodge--Tate--Taguchi filtration. Using this update, we establish a transcendence characterization of equicharacteristic local shtukas with abelian Tannakian structure group, matching a result of Howe--Klevdal in the p-adic setting. A special case of this result says that a formal Drinfeld module over an equicharacteristic local field has complex multiplication if and only if the Hodge--Tate--Taguchi filtration on its z-adic Tate module is algebraic.

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Cite

BibTeXRIS
BibTeX
@misc{cheng2026hartls,
  title = {{Hartl's dictionary and a transcendence characterization of equicharacteristic local shtukas with complex multiplication}},
  author = {Minhua Cheng and Sean Howe},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34822},
  eprint = {2610.34822},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34822},
}
RIS
TY  - UNPB
TI  - Hartl's dictionary and a transcendence characterization of equicharacteristic local shtukas with complex multiplication
AU  - Minhua Cheng
AU  - Sean Howe
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.34822
UR  - https://arxiv.org/abs/2610.34822
AB  - We update Hartl's dictionary between p-adic Hodge theory and its equicharacteristic analog to include aspects related to the Hodge--Tate filtration in p-adic Hodge theory and its equicharacteristic analog, the Hodge--Tate--Taguchi filtration. Using this update, we establish a transcendence characterization of equicharacteristic local shtukas with abelian Tannakian structure group, matching a result of Howe--Klevdal in the p-adic setting. A special case of this result says that a formal Drinfeld module over an equicharacteristic local field has complex multiplication if and only if the Hodge--Tate--Taguchi filtration on its z-adic Tate module is algebraic.
ER  -