The Total Rank Conjecture in Characteristic Two
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909166165032960 |
|---|---|
| author | VandeBogert, Keller Walker, Mark E. |
| author_facet | VandeBogert, Keller Walker, Mark E. |
| contents | The Total Rank Conjecture is a coarser version of the Buchsbaum-Eisenbud-Horrocks conjecture which, loosely stated, predicts that modules with large annihilators must also have ``large'' syzygies. This conjecture was proved by the second author for rings of odd characteristic by taking advantage of the Adams operations on the category of perfect complexes with finite length homology. In this paper, we prove a stronger form of the Total Rank Conjecture for rings of characteristic two. This result may be seen as evidence that the Generalized Total Rank Conjecture (which is known to be false in odd characteristic) actually holds in characteristic two. We also formulate a meaningful extension of the Total Rank Conjecture over non Cohen-Macaulay rings and prove that this conjecture holds for any ring containing a field (independent of characteristic). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09771 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Total Rank Conjecture in Characteristic Two VandeBogert, Keller Walker, Mark E. Commutative Algebra Algebraic Topology 13D02 The Total Rank Conjecture is a coarser version of the Buchsbaum-Eisenbud-Horrocks conjecture which, loosely stated, predicts that modules with large annihilators must also have ``large'' syzygies. This conjecture was proved by the second author for rings of odd characteristic by taking advantage of the Adams operations on the category of perfect complexes with finite length homology. In this paper, we prove a stronger form of the Total Rank Conjecture for rings of characteristic two. This result may be seen as evidence that the Generalized Total Rank Conjecture (which is known to be false in odd characteristic) actually holds in characteristic two. We also formulate a meaningful extension of the Total Rank Conjecture over non Cohen-Macaulay rings and prove that this conjecture holds for any ring containing a field (independent of characteristic). |
| title | The Total Rank Conjecture in Characteristic Two |
| topic | Commutative Algebra Algebraic Topology 13D02 |
| url | https://arxiv.org/abs/2305.09771 |