Serre's Conjecture II (Algebra)
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High Quality Content by WIKIPEDIA articles! In mathematics, Jean-Pierre Serre conjectured the following result regarding the Galois cohomology of a simply connected semisimple algebraic group. Namely, he conjectured that if G is such a group over a field F of cohomological dimension at most 2, then the Galois cohomology set H1(F, G) is zero. The conjecture holds in the case where F is a local field (such as p-adic field) or a global field with no real embeddings (such as Q( 1)). This is a special case of the Kneser Harder Chernousov Hasse Principle for algebraic groups over global fields. (Not...
High Quality Content by WIKIPEDIA articles! In mathematics, Jean-Pierre Serre conjectured the following result regarding the Galois cohomology of a simply connected semisimple algebraic group. Namely, he conjectured that if G is such a group over a field F of cohomological dimension at most 2, then the Galois cohomology set H1(F, G) is zero. The conjecture holds in the case where F is a local field (such as p-adic field) or a global field with no real embeddings (such as Q( 1)). This is a special case of the Kneser Harder Chernousov Hasse Principle for algebraic groups over global fields. (Note that such fields do indeed have cohomological dimension at most 2.) The conjecture also holds when F is finitely generated over the complex numbers and has transcendence degree at most 2.
