Witt groups of quadrics and hermitian forms over Clifford algebras
| dc.contributor.author | Cisneros, Joaquin | |
| dc.date.accessioned | 2025-04-28T19:09:59Z | |
| dc.date.available | 2025-04-28T19:09:59Z | |
| dc.date.issued | 2025 | |
| dc.description.abstract | The algebraic theory of quadratic forms aims to understand the classification of quadratic forms over a general field. A major open problem in the subject is to determine those forms which split (i.e., become hyperbolic) after scalar extension to the function field of a quadric. As a first step, one can hope to examine the forms that already split over the quadric itself. In a 2018 paper, Heng Xie showed that these arise as quadratic traces of hermitian forms over the even Clifford algebra of the quadric (equipped with its canonical involution). The explicit determination of these trace forms, however, appears to be a difficult problem in general. The goal of this project will be to use the tensor product decomposition of the even Clifford algebra together with hermitian Morita equivalences in order to determine the traces in certain special but important cases. The initial focus will be on the case where the given quadric is excellent (e.g., defined by a sum of squares). | |
| dc.description.reviewstatus | Reviewed | |
| dc.description.scholarlevel | Undergraduate | |
| dc.description.sponsorship | Jamie Cassels Undergraduate Research Awards (JCURA) | |
| dc.identifier.uri | https://hdl.handle.net/1828/22037 | |
| dc.language.iso | en | |
| dc.publisher | University of Victoria | |
| dc.subject | quadratic | |
| dc.subject | bilinear | |
| dc.subject | Witt | |
| dc.subject | hermitian | |
| dc.subject | ring | |
| dc.subject | Clifford | |
| dc.title | Witt groups of quadrics and hermitian forms over Clifford algebras | |
| dc.type | Poster |