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The J-invariant and the Tits algebras of a linear algebraic group

Anne Quéguiner-Mathieu, Nikita Semenov, Kirill Zainoulline

Number 12
Author JunProf. Nikita Semenov
Year 2011

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.

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