Geodesic
A Finiteness Theorem for Special Unitary Groups of Quaternionic Skew-Hermitian Forms with Good Reduction
Documenta mathematica, Tome 25 (2020), pp. 1171-1194
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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.
DOI : 10.4171/dm/773
Classification : 11E72, 11R34, 14L15, 16K20
Mots-clés : Morita theory, algebraic groups, Galois cohomology, good reduction, unramified cohomology 
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     author = {Srimathy Srinivasan},
     title = {A {Finiteness} {Theorem} for {Special} {Unitary} {Groups} of {Quaternionic} {Skew-Hermitian} {Forms} with {Good} {Reduction}},
     journal = {Documenta mathematica},
     pages = {1171--1194},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/773},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/773/}
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Srimathy Srinivasan. A Finiteness Theorem for Special Unitary Groups of Quaternionic Skew-Hermitian Forms with Good Reduction. Documenta mathematica, Tome 25 (2020), pp. 1171-1194. doi: 10.4171/dm/773

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