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RATIONAL EQUIVALENCE ON ADJOINT GROUPS OF TYPE D<inf>n</inf> OVER FIELDS OF VIRTUAL COHOMOLOGICAL DIMENSION 2
Journal
Transactions of the American Mathematical Society
ISSN
00029947
Date Issued
2022-10-01
Author(s)
Archita, M.
Preeti, R.
Abstract
Let F be a field of characteristic different from 2 and such that virtual cohomological dimension of F is 2. Let G be a semisimple classical adjoint group of type Dn defined over F. We show that G(F)/R = 0, where R denotes rational equivalence on G(F). The analogous result for groups of type 1An and Bn has been proved by Merkurjev, for groups of type 2A2n by Voskresenskii-Klyachko and for general groups of type 2An and Cn by Kulshreshta-Parimala. Combining the main theorem of this paper with the above mentioned results, we have G(F)/R is trivial, for any semisimple adjoint classical group G defined over F.
Volume
375
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