一般交换交叉积中的不可分解p-代数和Galois子域
Indecomposable p-algebras and Galois subfields in generic abelian crossed products
摘要：
设F是一个Hensel值域，char（F）= p，D是一个半分歧的，“非强退化”的p-代数.我们证明了D的所有伽罗瓦子域都是惯性的。以此为工具，我们研究了一般交换交叉积p-代数，证明了由非退化矩阵定义的非循环一般交换交叉积p-代数是不可分解的p-代数.为了构造这些指数为p且指数为大的不可分解p-代数的例子，我们研究了定义交换交叉积的矩阵的退化性与Severi-Brauer簇CH ^2中的挠之间的关系。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
