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Homological stability has emerged over the past decades as an organizing principle in topology and beyond. Broadly speaking, many sequences of moduli spaces exhibit the striking phenomenon that their homology stabilizes as the underlying complexity...

The singularities of integral models of Shimura varieties are encoded in their local models, schemes over the $p$-adic integers whose special fibers are unions of affine Schubert cells. A fundamental question is whether these local models are Cohen...

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