On the generalised André–Pink–Zannier conjecture. by Richard, Rodolphe, Yafaev, Andrei

Subjects: “…Shimura varieties…”
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The field of moduli of quaternionic multiplication on abelian varieties by Victor Rotger

“…We consider principally polarized abelian varieties with quaternionic multiplication over number fields and we study the field of moduli of their endomorphisms in relation to the set of rational points on suitable Shimura varieties.…”
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Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials by Deroin, Bertrand, Matheus, Carlos

“…Partly inspired by the case of homogenous spaces carrying bi-algebraic structures (such as torii, Abelian varieties and Shimura varieties), Klingler and Lerer recently showed that any bi-algebraic curve in a stratum of the moduli space of Abelian differentials is linear provided that the so-called condition $(\star )$ is fulfilled.In this note, we construct a non-linear bi-algebraic curve, resp. surface, of Abelian differentials of genus $7$, resp. $10$.…”
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