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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.

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Generalization of the Castelnuovo-Severi inequality

The Castelnuovo-Severi says that given curves $X,Y,Z$ over a perfect field $k$ and nonconstant morphisms $f:X\rightarrow Y$ and $g:X \rightarrow Z$ which do not both factor through any morphism $X\rig …