Decomposable and indecomposable algebras of degree and exponent 2

作者：Barry Demba^*

来源：Mathematische Zeitschrift, 2014, 276(3-4): 1113-1132.

DOI：10.1007/s00209-013-1236-8

We study the decomposition of central simple algebras of exponent 2 into tensor products of quaternion algebras. We consider in particular decompositions in which one of the quaternion algebras contains a given quadratic extension. Let be a biquaternion algebra over with trivial corestriction. A degree 3 cohomological invariant is defined and we show that it determines whether has a descent to . This invariant is used to give examples of indecomposable algebras of degree and exponent 2 over a field of 2-cohomological dimension 3 and over a field where the -invariant of is and is an indeterminate. The construction of these indecomposable algebras uses Chow group computations provided by Merkurjev in "Appendix".

• 出版日期2014-4