STNB2025 (38th edition)
Comparing Galois Representations : a 3-adic example
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Ignasi Sánchez
Resumen
The Faltings-Serre-Livne method allows to prove if two $2$-dimensional, residually reducible $2$-adic representations are isomorphic by comparing traces at finitely many Frobenius. An extension of this method for $p$-adic representations of dimension $\geq 2$ was described by Grenier but no practical algorithm is available. In this talk we will discuss Grenier method and showcase an implementation by proving modularity of $3$-adic representation of an abelian surface.
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