E_{0} (Q_{p}) = {P : red (P) \in \overset{ˉ}{E}_{ns} (F_{p})},

and

E_{1} (Q_{p}) = ker (E_{0} (Q_{p}) \to \overset{ˉ}{E}_{ns} (F_{p})) .

For

r \geq 1

z = - x / y

and put

E_{r} (Q_{p}) = {P \in E_{1} (Q_{p}) : v_{p} (z (P)) \geq r} .

Reduction induces

E_{0} (Q_{p}) / E_{1} (Q_{p}) ≅ \overset{ˉ}{E}_{ns} (F_{p}),

while the coefficient of

p^{r}

in the formal parameter gives

E_{r} (Q_{p}) / E_{r + 1} (Q_{p}) ≅ (F_{p}, +) qq u a d (r \geq 1) .

Solved by gpt-5.6-sol high.

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