On the locus of 2-dimensional crystalline representations with a given reduction modulo p

Abstract : We consider the family of irreducible crystalline representations of dimension $2$ of ${\rm Gal}(\overline{\bf Q}_p/{\bf Q}_p)$ given by the $V_{k,a_p}$ for a fixed weight integer $k\geq 2$. We study the locus of the parameter $a_p$ where these representations have a given reduction modulo $p$. We give qualitative results on this locus and show that for a fixed $p$ and $k$ it can be computed by determining the reduction modulo $p$ of $V_{k,a_p}$ for a finite number of values of the parameter $a_p$.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01519169
Contributeur : Sandra Rozensztajn <>
Soumis le : vendredi 5 mai 2017 - 23:05:31
Dernière modification le : samedi 6 mai 2017 - 01:05:35

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  • HAL Id : hal-01519169, version 1
  • ARXIV : 1705.01060

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Citation

Sandra Rozensztajn. On the locus of 2-dimensional crystalline representations with a given reduction modulo p. 2017. <hal-01519169>

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