2 problems

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Chai's formal-torus conjecture for ordinary points on mod $p$ Shimura varieties
Chai's conjecture. Then $X$ is a Shimura subvariety.
Conjectureopenbi-algebraicity serre-tate-theory shimura-varietiesarXiv posted 2 days ago
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The arithmetically bi-algebraic conjecture for enlarged mixed Shimura varieties
Let $S$ be an algebraic variety over $\overline{\mathbb{Q}}$ whose uniformization $\mathcal{X}$ has a structure of algebraic variety over $\overline{\mathbb{Q}}$ . Suppose that $Y$ …
Conjectureopenbi-algebraicity shimura-varieties transcendencearXiv posted 2 days ago

Chai's formal-torus conjecture for ordinary points on mod ppp Shimura varieties