# An algorithm for computing the reduction of 2-dimensional crystalline representations of $\text{Gal}(\overline\mathbf{Q}_p/\mathbf{Q}_p)$

Abstract : We describe an algorithm to compute the reduction modulo p of a crystalline Galois representation of dimension 2 of $\text{Gal}(\overline\mathbf{Q}_p/\mathbf{Q}_p)$ with distinct Hodge-Tate weights via the semi-simple modulo p Langlands correspondence. We give some examples computed with an implementation of this algorithm in SAGE.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-01402378
Contributor : Sandra Rozensztajn <>
Submitted on : Thursday, November 24, 2016 - 3:53:57 PM
Last modification on : Tuesday, December 4, 2018 - 2:51:26 PM

### Citation

Sandra Rozensztajn. An algorithm for computing the reduction of 2-dimensional crystalline representations of $\text{Gal}(\overline\mathbf{Q}_p/\mathbf{Q}_p)$. International Journal of Number Theory, World Scientific Publishing, 2018, 14 (07), pp.1857 -- 1894. 〈10.1142/S1793042118501117〉. 〈hal-01402378〉

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