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Hermitian and quadratic forms over local classical crossed product orders

Y. Hatzaras;  Th. Theohari-Apostolidi — 2000

Colloquium Mathematicae

Let R be a complete discrete valuation ring with quotient field K, L/K be a Galois extension with Galois group G and S be the integral closure of R in L. If a is a factor set of G with values in the group of units of S, then (L/K,a) (resp. Λ =(S/R,a)) denotes the crossed product K-algebra (resp. crossed product R -order in A). In this paper hermitian and quadratic forms on Λ -lattices are studied and the existence of at most two irreducible non-singular quadratic Λ -lattices is proved (Theorem 3.5)....

On local weak crossed product orders

Th. Theohari-Apostolidi;  A. Tompoulidou — 2014

Colloquium Mathematicae

Let Λ = (S/R,α) be a local weak crossed product order in the crossed product algebra A = (L/K,α) with integral cocycle, and H = σ ∈ G a l ( L / K ) | α ( σ , σ - 1 ) ∈ S * the inertial group of α, for S* the group of units of S. We give a condition for the first ramification group of L/K to be a subgroup of H. Moreover we describe the Jacobson radical of Λ without restriction on the ramification of L/K.

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