1
$\begingroup$

In continuation to my question here, are there known effective bounds on the total number of semisimple $p$-adic Galois representations unramified outside a finite set of primes $S$, of dimension $d$, and pure of weight $w$.

Thanks in advance!

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ The key inputs of his proofs of finiteness is first using Hermite-Minkowski to bound the number of possible number fields having bounded degree and unramified outside of (primes above) a set of places $S$, and then using Chebotarev to find primes outside of (places above) $S$ to represent Frobenius. These bounds are effective (i.e., can be given explicitly if one wants to work through the arguments) but not typically useful, because they are enormous. What application do you have in mind? $\endgroup$
    – Stanley Yao Xiao
    Commented Jun 27 at 12:35

0

Reset to default

You must log in to answer this question.