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Finiteness theorems for potentially equivalent Galois representations: extension of Faltings finiteness criteria

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 نشر من قبل Plawan Das
 تاريخ النشر 2020
  مجال البحث
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We study the relationship between potential equivalence and character theory; we observe that potential equivalence of a representation $rho$ is determined by an equality of an $m$-power character $gmapsto Tr(rho(g^m))$ for some natural number $m$. Using this, we extend Faltings finiteness criteria to determine the equivalence of two $ell$-adic, semisimple representations of the absolute Galois group of a number field, to the context of potential equivalence. We also discuss finiteness results for twist unramified representations.



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