2012/10/24 by Adrian Vasiu, Vasiu, Adrian
Mathematics · #11G10 #11G18 #11G35 #14F30 #14F55 #14G15 #14K22 #14L05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT) #and 14L15 #math.AG #math.NT #math.RT #msc:11G10 #msc:11G18 #msc:11G35 #msc:14F30 #msc:14F55 #msc:14G15 #msc:14K22 #msc:14L05 #msc:14L15
paper · pdf · doi:10.48550/arxiv.1210.6629
55 pages
arxiv created 2012/10/24 · openalex publication_date 2012/10/24 · arxiv updated 2012/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the isogeny property for special fibres of integral canonical models of compact Shimura varieties of An, Bn, Cn, and Dn\dbR type. The approach used also shows that many crystalline cycles on abelian varieties over finite fields which are specializations of Hodge cycles, are algebraic. These two results have many applications. First, we prove a variant of the conditional Langlands--Rapoport conjecture for these special fibres. Second, for certain isogeny sets we prove a variant of the unconditional Langlands--Rapoport conjecture (like for many basic loci). Third, we prove that integral canonical models of compact Shimura varieties of Hodge type that are of An, Bn, Cn, and Dn\dbR type, are closed subschemes of integral canonical models of Siegel modular varieties.