0
$\begingroup$

Given a prime $p$ and a polynomial equation $f(x,y)=0$ with rational coefficients, I would like to obtain a precise description of the set of all numbers $y\in\mathbb Q_p$ such that the equation has a solution $x\in\mathbb Q_p$. Are there currently implemented methods for doing this?

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ It's a union of disks. To get a description of the disks, you need to know the description of the set of solutions to $f(x,y) \equiv 0 \pmod{p}$. What do mean by a description of that? $\endgroup$
    – Felipe Voloch
    Commented Sep 22, 2014 at 1:12
  • $\begingroup$ @FelipeVoloch, I mean the explicit description of this projection as a semi-algebraic subset of $\mathbb Q_p$, as defined, for instance, in Jan Denef's paper "p-adic semi-algebraic sets and cell decomposition". $\endgroup$
    – 352506
    Commented Sep 23, 2014 at 20:30

0

Reset to default

You must log in to answer this question.