L'invariant de Suslin en caractéristique positive

Details L'invariant de Suslin en caractéristique positive L'invariant de Suslin en caractéristique positive

2009-07-28

arxiv.org/abs/0907.4899v1

Mathematics

Algebraic Geometry

33 pages

Scientific paper

Pour une k-alg\`ebre simple centrale A d'indice inversible dans k, Suslin a d\'efini un invariant cohomologique de SK_1(A). Dans ce texte, nous g\'en\'eralisons cet invariant \`a toute k-alg\`ebre simple centrale par un rel\`evement de la caract\'eristique positive \`a la caract\'eristique 0. Pour pouvoir d\'efinir cet invariant, on a besoin des groupes de cohomologie des diff\'erentielles 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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