$K_2$ of Fermat curves with divisorial support at infinity

Raymond Ross

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We consider an irreducible curve $𝒞$ in $E^{n}$ , where $E$ is an elliptic curve and $𝒞$ and $E$ are both defined over $\bar{ℚ}$ . Assuming that $𝒞$ is not contained in any translate of a proper algebraic subgroup of $E^{n}$ , we show that the points of the union $⋃ 𝒞 \cap A (\bar{ℚ})$ , where $A$ ranges over all proper algebraic subgroups of $E^{n}$ , form a set of bounded canonical height. Furthermore, if $E$ has Complex Multiplication then the set $⋃ 𝒞 \cap A (\bar{ℚ})$ , for $A$ ranging over all algebraic subgroups of $E^{n}$ of codimension at least $2$ , is finite. If $E$ has no...

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In this paper, we survey some Galois-theoretic techniques for studying torsion points on curves. In particular, we give new proofs of some results of A. Tamagawa and the present authors for studying torsion points on curves with “ordinary good” or “ordinary semistable” reduction at a given prime. We also give new proofs of : (1) the Manin-Mumford conjecture : there are only finitely many torsion points lying on a curve of genus at least $2$ embedded in its jacobian by an Albanese map;...

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Displaying similar documents to “ K 2 of Fermat curves with divisorial support at infinity”

Displaying similar documents to “ $K_{2}$ of Fermat curves with divisorial support at infinity”