Some corrections from Bhupendra Nath Tiwari.
Elliptic Curves
p.31 (4.2) where g^{\star}(X,Y,Z)= ...
One see easily that ... One sees easily that ...
p.49 (Isogenies) Two elliptic curves...
Thus a regular map \verphi: E -> E^{\prime} is an asigeny if \verphi(O)= O^{\prime}
and \verphi (k^{al}): E^{al} -> E^{al} is surjective. --->
Thus a regular map \verphi: E -> E^{\prime} is an asigeny if \verphi(O)= O^{\prime}
and \verphi (k^{al}): E^{al} -> E^{\prime}^{al} is surjective.
p.66 (5.8) We now begin ...
After Proposition 4.2, ... ---> After corrolary 4.2, ...
p.73 (6.2) ... has an inverse image the curve
Y^2X^2= X^3 + a X , ... ---> Y^2X^2= X^3 + \alpha X , ...
p.89 (The notion of a Riemann surface) Let X be a connected ...
to be equivalent if the their union is also a coordinate covering ... --->
to be equivalent if their union is also a coordinate covering ...
p.97 (3.17 PROOF)
On eliminating $\alpha$ from between the two equations, we find that
c \tau^2+ (d-a)\tau + b=0 -----> c \tau^2+ (d-a)\tau -b =0
p.97 (3.17 PROOF)
... On eliminating $\tau$ from between the two equations, we find that
\alpha^2 -(a+d)\alpha +bc=0 ----> \alpha^2 -(a+d)\alpha +ad- bc=0
p.120 (4.2 PROOF) It remains to show that
max (| ac |, | ad + bc |, | bd |) \ge ½ (max( | a |, | b |) (max( | c | | d |) --->
max (| ac |, | ad + bc |, | bd |) \ge ½ (max( | a |, | b |) (max( | c |, | d |))
p.128 (5.4) (b) ... that the Pontryagin dual of this sequence is an exact sequence: ...
In this sequence, the \prod_{p, \infty} H^1(Q_p,E)---> \prod_{p= 2, \infty} H^1(Q_p,E)
p.134 A morphism ...
is simply a map A-sets. We ... ---> is simply a map of A-sets. We ...
p.134 (Twist of elliptic curves)
Recall (Theorem 2.1, Chap. I) that E(a,b) and ... --->
Recall (Theorem 2.1, Chap. II) that E(a,b) and ...
p.135 (7.12) In order to be able to apply...
We apply Theorem 2.1, Chap. I in the case (a^{\prime}, b^{\prime}) = (a, b). --->
We apply Theorem 2.1, Chap. II in the case (a^{\prime}, b^{\prime}) = (a, b).
p.141 (Curves of genus 1) Let \sigma \in \Gamma. ...
Now (see 2.3) there is a curve E_0.. ---> Now (see 2.3, Chap. II) there is a curve E_0 ...
p.149 (9.2 PROOF) ... is surjective (4.23). In particular, there exists a ... --->
... is surjective (4.23, Chap. I). In particular, there exists a ...
p.170 (Spha\ere Packing) Let E be a constant elliptic curve ...
then part (a) of Theorem 11.2 gives us r, ... ---> then part (a) of Proposition 11.1 gives us r, ...
p.171 (11.4 PROOF) Since all \alpha_i and \omega_j equal -q,
if follows from (11.2a) that ... ---> it follows from (11.1a) that ...
p.174 (1.1) For example, ..
whose in inverse C^{\times} -> C/Z is ... ---> whose inverse in C^{\times} -> C/Z is ...
p.193. (3.7 PROOF) From the theorem, we know that ...
of \Delta, and it will be follow from the ... ---> of \Delta, and it will follow from the ...
p.195. (4.1 PROOF) then
(\alpha \verphi) (x: y:z) = (P(x^p, y^p, z^p), ...) and
(\verphi \alpha) (x: y:z) = (P(x, y, z)^p, ...) --->
(\alpha \verphi) (x: y:z) = (P(x^p, y^p, z^p): ...) and
(\verphi \alpha) (x: y:z) = (P(x, y, z)^p: ...)
(in the rhs of these Eqns, the , in outer brackets should be :)
p.199 (4.7) The maps T(n) have the having the following properties: --->
The maps T(n) have the following properties:
p.212 where both are defined. ...
One can check that it also holomorphic at the point at infinity. --->
One can check that it is also holomorphic at the point at infinity.
p.215 Now suppose X is a...
over an field k. Weil showed ... ---> over a field k. Weil showed ...
p.219 When i \ne 0, ...
... where \tilde{E}_i/ \tilde{E}/S_i and ... --->
... where \tilde{E}_i= \tilde{E}/S_i and ...
General: Some places you need to replace df by def, or add in the list of notation: def=df.