Simple proofs of classical explicit reciprocity laws on curves using determinant groupoids over an artinian local ring
| dc.creator | Anderson, Greg W. | |
| dc.creator | Romo, Fernando Pablos | |
| dc.date | 2002-07-31 | |
| dc.date.accessioned | 2026-07-07T04:49:58Z | |
| dc.date.available | 2026-07-07T04:49:58Z | |
| dc.description | The notion of determinant groupoid is a natural outgrowth of the theory of the Sato Grassmannian and thus well-known in mathematical physics. We briefly sketch here a version of the theory of determinant groupoids over an artinian local ring, taking pains to put the theory in a simple concrete form suited to number-theoretical applications. We then use the theory to give a simple proof of a reciprocity law for the Contou-Carrère symbol. Finally, we explain how from the latter to recover various classical explicit reciprocity laws on nonsingular complete curves over an algebraically closed field, namely sum-of-residues-equals-zero, Weil reciprocity, and an explicit reciprocity law due to Witt. Needless to say, we have been much influenced by the work of Tate on sum-of-residues-equals-zero and the work of Arbarello-DeConcini-Kac on Weil reciprocity. We also build in an essential way on a previous work of the second-named author. | |
| dc.identifier | https://arxiv.org/abs/math/0207311 | |
| dc.identifier | http://arxiv.org/abs/math/0207311 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64635 | |
| dc.subject | Number Theory | |
| dc.title | Simple proofs of classical explicit reciprocity laws on curves using determinant groupoids over an artinian local ring | |
| dc.type | text |