Good Reduction of Good Filtrations at Places

On the Fiber Cones of Good Filtrations

Let A be a Noetherian local ring with the maximal ideal m and an m-primary ideal J . Let F = {In}n≥0 be a good filtration of ideals in A. Denote by FJ (F) = ⊕ n≥0 (In/JIn)t n the fiber cone of F with respect to J. The paper characterizes the multiplicity and the CohenMacaulayness of FJ (F) in terms of minimal reductions of F .

GOOD l-FILTRATIONS FOR q − GL3(k)

Let k be an algebraically closed field of characteristic p, possibly zero, and G = qGL3(k), the quantum group of three by three matrices as defined by Dipper and Donkin. We may also take G to be GL3(k). We first determine the extensions between simple G-modules for both G and G1, the first Frobneius kernel of G. We then determine the submodule structure of certain induced modules, Ẑ(λ), for the...

Good filtrations and F -purity of invariant subrings

Let k be an algebraically closed field of positive characteristic, G a reductive group over k, and V a finite dimensional G-module. Let B be a Borel subgroup of G, and U its unipotent radical. We prove that if S = SymV has a good filtration, then SU is F -pure. Throughout this paper, p denotes a prime number. Let k be an algebraically closed field of characteristic p, and G a reductive group ov...

Good reduction of abelian varieties

Potentially Good Reduction of Barsotti-tate Groups

Let R be a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, K the fraction field of R. Suppose G is a Barsotti-Tate group (p-divisible group) defined over K which acquires good reduction over a finite extension K′ of K. We prove that there exists a constant c ≥ 2 which depends on the absolute ramification index e(K′/Qp) and the height of G such that G ...