On the locus of $2$-dimensional crystalline representations with a given reduction modulo $p$
| Autor: | Rozensztajn, Sandra |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Alg. Number Th. 14 (2020) 643-700 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/ant.2020.14.655 |
| Popis: | 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 $a_p$. We also generalize these results to other Galois types. Comment: to appear in Algebra & Number Theory |
| Databáze: | arXiv |
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