Torsion Points on Curves
نویسندگان
چکیده
EXAMPLES. (i) The multiplicative group A = Gm is the algebraic group whose points over a field are the nonzero elements of the field. Then for any field K, Tor Gm(K) are the roots of unity contained in K. (ii) A = Gm×Gm then Tor(A) = Tor(Gm)×Tor(Gm) = {(x, y) : x, y ∈ K are roots of unity}. (iii) Let A be an elliptic curve. Over the complex numbers we can uniformize A as A = C/L where L is a lattice. Then Tor(A(C)) = Q ⊗ L/L.
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