On Shafarevich-Tate groups and the arithmetic of Fermat Curves

William G. McCallum; Pavlos Tzermias

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On Shafarevich-Tate groups and the arithmetic of Fermat Curves

William G. McCallum·Pavlos Tzermias

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Abstract

We extend the results of the first author on nontrivial elements in the Shafarevich-Tate group of the jacobian of a quotient of a Fermat curve of prime degree, and use the methods of the second author to derive a result bounding the quadratic points on the Fermat curve of degree 19.

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William G. McCallum, Pavlos Tzermias. 2002-10-31. On Shafarevich-Tate groups and the arithmetic of Fermat Curves. https://arxiv.org/abs/math/0210483

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