Hecke eigensystems of automorphic forms (mod $p$) of Hodge type and algebraic modular forms

Abstract

We show that the systems of prime-to-$p$ Hecke eigenvalues arising from automorphic forms$(\mathrm{mod}p)$ for a good prime $p$ associated to an algebraic group $G/\mathbb{Q}$ of Hodge type are the same as those arising from algebraic modular forms$(\mathrm{mod}p)$ associated to an inner form of $G$.

Shortened revised version, 27 pages, to appear in Math. Ann. Comments are welcome

References in corpus (4)

• Rapoport-Zink spaces for spinor groups
• Cycles on Shimura varieties via geometric Satake
• Stratifications and foliations for good reductions of Shimura varieties of Hodge type
• Polarized superspecial simple abelian surfaces with real Weil numbers