A Limiting Version of a Theorem in Cohomology
| dc.creator | Eesanaipaadi, Venkata Balaji Thiruvalloor | |
| dc.date | 2004-07-06 | |
| dc.date.accessioned | 2026-07-07T05:09:58Z | |
| dc.date.available | 2026-07-07T05:09:58Z | |
| dc.description | Scheme-theoretic methods are used to classify ternary quadratic forms with values in line bundles over arbitrary schemes and to canonically determine the isomorphisms between them. The association of a quadratic bundle to its even Clifford algebra induces a natural bijection from the set of equivalence classes of line-bundle-valued quadratic forms on rank 3 vector bundles upto tensoring by twisted discriminant bundles and the set of isomorphism classes of schematic specialisations of rank 4 Azumaya bundles over any fixed scheme X. This statement is a limiting version of the following statement: the set of orbits of Disc(X) in the 1-cohomology of X in the fppf topology with values in O(3) is in bijection with the 1-cohomology with values in PGL(2). The various orthogonal groups of a quadratic bundle are canonically determined in terms of the automorphisms of its even Clifford algebra. Any automorphism of the latter arises from a similarity, and in fact from an orthogonal transformation if its determinant is a square. The special orthogonal group is thus identified with the subgroup of automorphisms with trivial determinant. A specialised algebra arises from a honest quadratic form iff its determinant has a square root and arises from a bilinear form iff the line subbundle generated by 1 is a direct summand. | |
| dc.description | Dedicated to Professor Martin Kneser (13p.) Keywords: semiregular form, quadratic bundle, Azumaya bundle, Witt-invariant, line-bundle-valued form, Clifford algebra, discriminant bundle, orthogonal group, similarity, similitude | |
| dc.identifier | https://arxiv.org/abs/math/0407079 | |
| dc.identifier | http://arxiv.org/abs/math/0407079 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71786 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Rings and Algebras | |
| dc.subject | 11Exx, 11E12, 11E20, 11E88, 11R52, 14L15, 15A63, 16S, 16H05 | |
| dc.title | A Limiting Version of a Theorem in Cohomology | |
| dc.type | text |