Non-compact form of the Elementary Discrete Invariant
We determine the non-compact form of Vishik's Elementary Discrete Invariant for quadrics.
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arXiv subjects
Raphaël Fino
Publications and source records attributed to Raphaël Fino.
$J$-invariant of hermitian forms over quadratic extensions
We develop the version of the $J$-invariant for hermitian forms over quadratic extensions in a similar way Alexander Vishik did it for quadratic forms. This discrete invariant contains informations about rationality of algebraic cycles on the maximal unitary grassmannian associated with a hermitan form over a quadratic extension. The computation of the canonical $2$-dimension of this grassmannian in terms of the $J$-invariant is provided, as well as a complete motivic decomposition.
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Symmetric correspondences on quadrics
We prove a result comparing the rationality of some elementary algebraic cycles introduced by Alexander Vishik, defined on orthogonal grassmannians, with the rationality of some algebraic cycles defined on fiber products of the corresponding quadric.
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Rationality of cycles over function fields of $SL_1(A)$-torsors
In this note we prove a result comparing rationality of algebraic cycles over the function field of a $SL_1(A)$-torsor for a central simple algebra $A$ and over the base field.
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Around rationality of integral cycles
In this article we prove a result comparing rationality of integral algebraic cycles over the function field of a quadric and over the base field. This is an integral version of the result known for coefficients modulo 2. Those results have already been proved by Alexander Vishik in the case of characteristic 0, which allowed him to work with algebraic cobordism theory. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic different from 2.
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