A Reply
Zhou Xueguang
September 22, 2003
As I think that your argument on D. Ravenel's proof of non-existence of
V(3) at p=5 is incorrect (top of P.5 on your paper). Sure we could not get
the conclusion that dr(fl3) 6= 0 from fi1716= 0. But D. Ravenel's idea is as
following.
Firstly, he proved that fi211= 0, (indeed it is a result from Toda) and
d33(ff1fi45=5) = fi211. Then he says that ff1fi45=5is a linear combination of f*
*i31fl3,
3_fi31fi14 and fi1x761, i.e. ff1fi45=5= k1fi31fl3 + k23_fi31fi14+ k3fi1x761. *
*But 3_fi31fi14
and fi1x761are permanent cycles. So
d33(k1fi31fl3 + k23_fi31fi14+ k3fi1x761) = d33(k1fi31fl3) = fi211
And then k1 6= 0 and
d33(k1fi31fl3) = k1fi31d33(fl3) = fi211
Sure I did not check his computation. Maybe Nakai who is at Rochester
now did. As K. Shimomura says, he did not check D. Ravenel's computation
neither, but D. Ravenel is computing ßn(S0) at p = 5 whthin n 6000 lately.
So he might recomputed that.
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