An explicit universal blowup process on a birational Grassmannian model is claimed to simultaneously resolve every integral singular Γ-scheme over Q and over finite fields.
Resolution of Singularities in Arbitrary Characteristic
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abstract
Let $X$ be an integral affine or projective scheme of finite presentation over a perfect field. We prove that $X$ admits a resolution, that is, there exists a smooth scheme $\widetilde X$ and a projective birational morphism from $\widetilde X$ onto $X$.
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Universal Characteristic-free Resolution of Singularities, I
An explicit universal blowup process on a birational Grassmannian model is claimed to simultaneously resolve every integral singular Γ-scheme over Q and over finite fields.