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Sur les invariants cohomologiques des groupes algébriques linéaires

Abstract : Our thesis deals with the cohomological invariants of smooth and connected linear algebraic groups over an arbitrary field. More precisely, we study degree 2 invariants with coefficients Q/Z(1), that is invariants taking values in the Brauer group. Our main tool is the étale cohomology of sheaves on simplicial schemes. We get a description of these invariants for every smooth and connected linear groups, in particular for non reductive groups over an imperfect field (as pseudo-reductive or unipotent groups for instance).We use our description to investigate how the groups of invariants with values in the Brauer group behave with respect to operations on algebraic groups. We detail this group of invariants for particular non reductive algebraic groups over an imperfect field
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Submitted on : Monday, July 6, 2020 - 10:39:28 AM
Last modification on : Wednesday, July 15, 2020 - 10:36:24 AM
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Alexandre Lourdeaux. Sur les invariants cohomologiques des groupes algébriques linéaires. Théorie des groupes [math.GR]. Université de Lyon, 2020. Français. ⟨NNT : 2020LYSE1044⟩. ⟨tel-02890182⟩



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