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arxiv: 0705.3860 · v1 · submitted 2007-05-25 · 🧮 math.RA

Indecomposable p-algebras and Galois subfields in generic abelian crossed products

classification 🧮 math.RA
keywords p-algebrasabeliancrossedgenericindecomposablegaloismatricesproduct
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Let F be a Henselian valued field with char(F) = p and D a semi-ramified, "not strongly degenerate" p-algebra. We show that all Galois subfields of D are inertial. Using this as a tool we study generic abelian crossed product p-algebras, proving among other things that the noncyclic generic abelian crossed product p-algebras defined by non-degenerate matrices are indecomposable p-algebras. To construct examples of these indecomposable p-algebras with exponent p and large index we study the relationship between degeneracy in matrices defining abelian crossed products and torsion in CH^2 of Severi-Brauer varieties.

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