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

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Moduli spaces of arithmetic varieties with isomorphic $l$-adic cohomology

Given a positive integer $d$, a rational prime $l$ and a number field $K$, is it sensible to consider the moduli stack of $d$-dimensional varieties over $K$ whose $l$-adic cohomology rings are isomorp …