Journal of the Ramanujan Mathematical Society

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Index Reduction Formula


Affiliations
1 Department of Mathematics and Mechanics, St.Petersburg State University, St.Petersburg, Petrodvorets, 198904, Russian Federation
     

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Let C be a reductive algebraic group over a field F, such that Pic(G ®F L) = 0 for any field extension L/F, Xa homogeneous variety of G over F, D a central simple F-algebra. We give an index reduction formula for the index of D over the function field F ( X) in terms of indexes of certain algebras, associated to X, and dimensions of certain representations of the stabilizer of a point in X. This formula generalizes the known ones in the cases of projective homogeneous varieties and principal homogeneous spaces.
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  • Index Reduction Formula

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Authors

A. S. Merkurjev
Department of Mathematics and Mechanics, St.Petersburg State University, St.Petersburg, Petrodvorets, 198904, Russian Federation

Abstract


Let C be a reductive algebraic group over a field F, such that Pic(G ®F L) = 0 for any field extension L/F, Xa homogeneous variety of G over F, D a central simple F-algebra. We give an index reduction formula for the index of D over the function field F ( X) in terms of indexes of certain algebras, associated to X, and dimensions of certain representations of the stabilizer of a point in X. This formula generalizes the known ones in the cases of projective homogeneous varieties and principal homogeneous spaces.