## Tate module and bad reduction

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- by Tim Dokchitser, Vladimir Dokchitser and Adam Morgan PDF
- Proc. Amer. Math. Soc.
**149**(2021), 1361-1372 Request permission

## Abstract:

Let $C/K$ be a curve over a local field. We study the natural semilinear action of Galois on the minimal regular model of $C$ over a field $F$ where it becomes semistable. This allows us to describe the Galois action on the $l$-adic Tate module of the Jacobian of $C/K$ in terms of the special fibre of this model over $F$.## References

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## Additional Information

**Tim Dokchitser**- Affiliation: Department of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
- MR Author ID: 733080
- Email: tim.dokchitser@bristol.ac.uk
**Vladimir Dokchitser**- Affiliation: Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom
- MR Author ID: 768165
- Email: v.dokchitser@ucl.ac.uk
**Adam Morgan**- Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
- MR Author ID: 1312165
- Email: a.j.morgan44@gmail.com
- Received by editor(s): February 13, 2019
- Received by editor(s) in revised form: February 4, 2020, and February 14, 2020
- Published electronically: February 11, 2021
- Additional Notes: This research was supported by EPSRC grants EP/M016838/1 and EP/M016846/1 ‘Arithmetic of hyperelliptic curves’. The second author was supported by a Royal Society University Research Fellowship.
- Communicated by: Rachel Pries
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 1361-1372 - MSC (2020): Primary 11G20; Secondary 11G25, 14F20, 11G07, 11G10
- DOI: https://doi.org/10.1090/proc/15067
- MathSciNet review: 4242296