Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778320 | Advances in Mathematics | 2017 | 81 Pages |
Abstract
We improve homology stability ranges for elementary and special linear groups over rings with many units. Our result implies stability for unstable Quillen K-groups and proves a conjecture of Bass. For commutative local rings with infinite residue fields, we show that the obstruction to further stability is given by Milnor-Witt K-theory. As an application we construct Euler classes of projective modules with values in the cohomology of the Milnor-Witt K-theory sheaf. For d-dimensional commutative noetherian rings with infinite residue fields we show that the vanishing of the Euler class is necessary and sufficient for an oriented projective module P of rank d to split off a rank 1 free direct summand. Along the way we obtain a new presentation of Milnor-Witt K-theory and of symplectic K2 simplifying the classical Matsumoto-Moore presentation.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Marco Schlichting,