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Showing 1 to 4 of 4 for “"torsion subgroups"”.
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Bounds on the Torsion Subgroups of Néron–Severi Groups
… we give an upper bound on the order of the torsion subgroup of second cohomology groups of 𝑋 and the finite group [mathematical equation]. We also show that (NS 𝑋)ₜₒᵣ is generated by (deg 𝑋 − 1)(deg 𝑋 − 2) elements in various situations.
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Torsion Subgroups Of Rational Elliptic Curves Over Odd Degree Galois Fields
… the rank of E and E(K)_tors is the subgroup of torsion points on E. Unfortunately, very little is known about the rank r_K. Even in the case of K = Q, it is not known which ranks are possible or if the ranks are bounded. However, there have been great strides in determining the sets E(K)_tors. …
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Torsion Subgroups of Rational Elliptic Curves Over Odd Degree Galois Fields
… the rank of E and E(K)_tors is the subgroup of torsion points on E. Unfortunately, very little is known about the rank r_K. Even in the case of K = Q, it is not known which ranks are possible or if the ranks are bounded. However, there have been great strides in determining the sets E(K)_tors. …
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Explicit moduli spaces for curves of genus 1 and 2
… is, we study pairs of elliptic curves whose $N$-torsion subgroups are isomorphic as Galois modules. In particular, we study the moduli surfaces $Z_{N,r}$ which parametrise $N$-congruences of elliptic curves which raise the Weil pairing to a power of $r$. We first study the birational geometry of …