WHITEHEAD GROUPS, REDUCED NORMS AND CYCLICITY OF SOME SPECIAL AZUMAYA ALGEBRAS
Abstract
We describe the multiplicative structure and the reduced norms for central division k-algebras A in the two following cases: (i) let k be a completion of the function field of the p-adic curve with respect to discrete valuations with finite extensions of Qp as residue fields and let A be tamely ramified division k-algebra; (ii) let A be skew-fields of non-commutative rational functions over p-adic division algebras. We also obtain some sufficient conditions for cyclicity of algebras from (i). In particular we prove that any algebra of square-free index from (i) is cyclic.
About the Author
V. I. Yanchevskiĭ
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
References
1. Draxl, P. SK1 von Schiefkorpern / P. Draxl, M. Kneeser // Lectures Notes Math. – 1977. – Vol. 778. – P. 1–124.
2. Merkurjev, A. S. Suslin’s conjecture on the reduced Whitehead group of a simple algebrs / A. S. Merkurjev // J. Amer. Math. Soc. Published electronically. – 2015. – November 17.
3. Saltman, D. Cyclic algebras over p-adic curves / D. Saltman // J. Algebra. – 2007. – Vol. 314. – P. 817–843.
4. Янчевский, В. И. Приведенные нормы простых алгебр над функциональными полями / В. И. Янчевский // Тр. МИАН СССР. – 1990. – Т. 183. – С. 215–222.
5. Янчевский, В. И. Приведенная унитарная K-теория и тела над гензелевыми дискретно нормированными полями / В. И. Янчевский // Изв. АН СССР. Сер. математика. – 1978. – Т. 42, № 4. – С. 879–918.
6. Yanchevskii, V. I. Reduced unitary Whitehead groups of skew fields of noncommutative rational functions / V. I. Yanchevskii // J. of Sov. Mathematics. – 1982. – Vol. 19, iss. 1. – P. 1067–1071.
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