Geodesic
A Finiteness Theorem for Special Unitary Groups of Quaternionic Skew-Hermitian Forms with Good Reduction
Documenta mathematica, Tome 25 (2020), pp. 1171-1194.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Given a field $K$ equipped with a set of discrete valuations $V$, we develop a general theory to relate reduction properties of skew-hermitian forms over a quaternion $K$-algebra $Q$ to quadratic forms over the function field $K(Q)$ obtained via Morita equivalence. Using this we show that if $(K,V)$ satisfies certain conditions, then the number of $K$-isomorphism classes of the universal coverings of the special unitary groups of quaternionic skew-hermitian forms that have good reduction at all valuations in $V$ is finite and bounded by a value that depends on size of a quotient of the Picard group of $V$ and the size of the kernel and cokernel of residue maps in Galois cohomology of $K$ with finite coefficients. As a corollary we prove a conjecture of Chernousov, Rapinchuk, Rapinchuk for groups of this type.
Classification : 11E72, 16K20, 11R34, 14L15
Keywords: algebraic groups, good reduction, Galois cohomology, unramified cohomology, Morita theory 
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     author = {Srinivasan, Srimathy},
     title = {A {Finiteness} {Theorem} for {Special} {Unitary} {Groups} of {Quaternionic} {Skew-Hermitian} {Forms} with {Good} {Reduction}},
     journal = {Documenta mathematica},
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     language = {en},
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Srinivasan, Srimathy. A Finiteness Theorem for Special Unitary Groups of Quaternionic Skew-Hermitian Forms with Good Reduction. Documenta mathematica, Tome 25 (2020), pp. 1171-1194. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a34/