Finite Weil restriction of curves

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• 作者：E. V. Flynn ; D. Testa
• 关键词：Higher genus curves ; Jacobians ; Weil restriction ; Primary 11G30 ; Secondary 11G10 ; 14H40
• 刊名：Monatshefte für Mathematik
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：176
• 期：2
• 页码：197-218
• 全文大小：257 KB
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  19. Schinzel, A.: Selected Topics on Polynomials. Univer
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081

文摘

Given number fields \(L \supset K\) , smooth projective curves? \(C\) defined over \(L\) and? \(B\) defined over \(K\) , and a non-constant \(L\) -morphism \(h :C \rightarrow B_{L}\) , we denote by \(C_{h}\) the curve defined over? \(K\) whose \(K\) -rational points parametrize the \(L\) -rational points on? \(C\) whose images under? \(h\) are defined over? \(K\) . We compute the geometric genus of the curve \(C_{h}\) and give a criterion for the applicability of the Chabauty method to find the points of the curve \(C_{h}\) . We provide a framework which includes as a special case that used in Elliptic Curve Chabauty techniques and their higher genus versions. The set \(C_{h}(K)\) can be infinite only when? \(C\) has genus at most?1; we analyze completely the case when? \(C\) has genus?1.