Integral canonical models for G-bundles on Shimura varieties of abelian type
Citation
Lovering, Thomas. 2017. Integral canonical models for G-bundles on Shimura varieties of abelian type. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.Abstract
This thesis builds on Kisin's theories of S-modules and integral models for Shimura varieties of abelian type to further our understanding of the arithmetic of Shimura varieties in several directions. First, we show that Shimura varieties ShK(G;X) of abelian type with level K hyperspecial at primes away from N and reflex field E admit canonical smooth integral models over OE[1/N]. Next, under the condition that Z(G) is split by a CM field, we prove that the standard principal G-bundles PK(G;X) also admit canonical integral models over OE[1/N], which are characterised uniquely using the theory of S-modules, and these in turn give rise to integral models for automorphic vector bundles. Finally, working over p-adic completions of Kisin's models, and dropping the restriction on Z(G) by working more purely with p-adic Hodge theory, we construct similarly canonical families of filtered F-crystals with G-structure. We then use these to deduce that the Galois representations arising in the p-adic cohomology of Shimura varieties with nontrivial coefficient sheaves are crystalline when the level is hyperspecial at p in the case of proper Shimura varieties of abelian type.Terms of Use
This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAACitable link to this page
http://nrs.harvard.edu/urn-3:HUL.InstRepos:41142070
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