Submission: 2011, Apr 8
In the present paper we set up a connection between the indices of the Tits algebras of a simple linear algebraic group G and the degree one parameters of its J-invariant. Our main technical tool is the second Chern class map in the Riemann-Roch theorem without denominators. As an application we recover some known results on the J-invariant of quadratic forms of small dimension; we describe all possible values of the J-invariant of an algebra with involution up to degree 8 and give explicit examples; we establish several relations between the J-invariant of an algebra A with involution and the J-invariant (of the quadratic form) over the function field of the Severi-Brauer variety of A.
2010 Mathematics Subject Classification: 20G15, 14C25, 14L30, 16W10, 11E04
Keywords and Phrases: linear algebraic group, algebra with involution, Tits algebra, motivic decomposition, torsor
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