UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

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Author: search.filters.author.Wilson, Kevin Michael

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    A Tannakian Description for Parahoric Bruhat-Tits Group Schemes
    (2010) Wilson, Kevin Michael; Haines, Thomas; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Let K be a field which is complete with respect to a discrete valuation and let O be the ring of integers in K. We study the Bruhat-Tits building B(G) and the parahoric Bruhat-Tits group schemes GF associated to a connected reductive split linear algebraic group G defined over O. In order to study these objects we use the theory of Tannakian duality, developed by Saavedra Rivano, which shows how to recover G from its category of finite rank projective representations over O. We also use Moy-Prasad filtrations in order to define lattice chains in any such representation. Using these two tools, we give a Tannakian description to B(G). We also define a functor AutF associated to a facet F in B(G) in terms of lattice chains in a Tannakian way. We show that AutF is representable by an affine group scheme of finite type, has the same generic fiber as G, and satisfies AutF(OE) = GF (OE) for every unramified Galois extension E of K. Moreover, we show that there is a canonical morphism from GF to AutF, which we conjecture to be an isomorphism. We prove that it is an isomorphism when the residue characteristic of K is zero and G is arbitrary, when G = GLn and K is arbitrary, and when F is the minimal facet containing the origin and G and K are arbitrary.