Canonical subgroups of generalized Drinfeld modules

Abstract

We study basic properties of canonical subgroups of generalized Drinfeld modules over a complete valuation ring of positive characteristic. In particular, we study the quotients of generalized Drinfeld modules by the canonical subgroups, and compute the valuations of the Hasse invariants and describe the canonical subgroups of these quotients. Moreover, we construct higher level canonical subgroups.

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Acknowledgements

The author is grateful to Urs Hartl for valuable discussions on the topics of this paper. He would like to thank the anonymous referee for careful reading of the paper and giving many helpful comments. He would also like to thank Chia-Fu Yu for supporting his postdoctoral studies. He also acknowledges support of the DAAD-MoST PPP project “G-Shtukas: Geometry and Arithmetic” (MoST 108-2911-I-001-506).

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Correspondence to Yasuhiro Terakado.

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Terakado, Y. Canonical subgroups of generalized Drinfeld modules. Res. number theory 7, 8 (2021). https://doi.org/10.1007/s40993-020-00229-7

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