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

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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 CH2 of Severi-Brauer varieties.

Original languageEnglish
Pages (from-to)1887-1907
Number of pages21
JournalJournal of Algebra
Issue number5
StatePublished - Sep 1 2008


  • Chow group
  • Generic algebras
  • Indecomposable division algebras
  • Severi-Brauer varieties
  • Valued division algebras
  • p-algebras


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