ПРЕПРИНТ
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We establish integral $E_2$-degeneration for the Leray spectral sequence of toroidal compactifications of Hodge-type Shimura varieties over $\Spec(\mathbb{Z})$. Using cohomological purity and the extension property of integral canonical models, we construct a Hecke-equivariant cuspidal projector that integrally separates Eisenstein and cuspidal cohomology classes in degree one. An anisotropy--cuspidality equivalence is proven, linking boundary geometry to intersection cohomology and to Galois realizations of automorphic representations. Applications to special values of $L$-functions and to integral comparison theorems are discussed.
Kundnani R. T., Kant Sh., Alam K. 2025. Integral Cohomology and Cuspidal Projectors for Hodge-Type Shimura Varieties over $\Spec(\mathbb{Z})$. PREPRINTS.RU. https://doi.org/
