The Tate-linear conjecture for products of GSpin Shimura varieties

Let $f:X_0\to\mathscr{S}_{\mathbf{I},F_{\infty}}^{\operatorname{ord}}$ be a locally closed immersion, so that $X$ is a subvariety of $\mathscr{S}_{\mathbf{I},F_{\infty}}^{\operatorname{ord}}$ , and let $x\in X(F_{\infty})$ . Say that $X$ is Tate-linear at $x$ when its formal completion at $x$ has the Tate-linear property. The Tate-linear conjecture for products of GSpin Shimura varieties. If $X$ is Tate-linear at $x$ , then $X$ is special.

This is the explicit geometric formulation of the product-GSpin Tate-linear conjecture. The supplied passage gives no resolution status for it.

Equivalent formulations 1

Other statements of this same problem, merged from separate entries. Each is equivalent to the statement above — proving any one settles them all.

The Tate-linear conjecture for products of GSpin Shimura varieties
Let $(X,x)$ , $X_0$ , $f$ , and $\T_{f,x}$ be as in the source, with $f:X_0\to X$ and with $\T_{f,x}$ the associated Tate-linear formal object. Let $\X_{f,F_{\infty},\operatorname{red}}^{/x}$ denote the formal reduction associated with $f$ at $x$ . The Tate-linear conjecture for products of GSpin Shimura varieties. One should have
$\mathscr{X}_{f,\mathbb{F},\operatorname{red}}^{/x}=\mathscr{T}_{f,x}.$
The equality is the product-GSpin formulation of Tate-linearity used in the paper. The supplied passage does not give a resolution status for this particular formulation.
source: Ruofan Jiang, “p-adic monodromy and mod p unlikely intersections, I”, arXiv:2308.06854 (2025).

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Ruofan Jiang, “p-adic monodromy and mod p unlikely intersections, I”, arXiv:2308.06854 (2025).

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The Tate-linear conjecture for products of GSpin Shimura varieties

Equivalent formulations 1

The Tate-linear conjecture for products of GSpin Shimura varieties

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