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arXiv · 0907.4899

L'invariant de Suslin en caractéristique positive

Tim Wouters
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Abstract

Pour une k-algèbre simple centrale A d'indice inversible dans k, Suslin a défini un invariant cohomologique de SK_1(A). Dans ce texte, nous généralisons cet invariant à toute k-algèbre simple centrale par un relèvement de la caractéristique positive à la caractéristique 0. Pour pouvoir définir cet invariant, on a besoin des groupes de cohomologie des différentielles logarithmiques de Kato. For a central simple k-algebra A with index invertible in k, Suslin defined a cohomological invariant for SK_1(A). In this text, we generalise his invariant to any central simple k-algebra using a lift from positive characteristic to characteristic 0. To be able to define the invariant, we use Kato's cohomology of logarithmic differentials.

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Tim Wouters. 2009-07-28. L'invariant de Suslin en caractéristique positive. https://arxiv.org/abs/0907.4899

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