On the arithmetic of tight closure
| dc.creator | Brenner, Holger | |
| dc.creator | Katzman, Mordechai | |
| dc.date | 2004-12-01 | |
| dc.date | 2004-12-02 | |
| dc.date.accessioned | 2026-07-07T05:14:53Z | |
| dc.date.available | 2026-07-07T05:14:53Z | |
| dc.description | We provide a negative answer to an old question in tight closure theory by showing that the containment x^3y^3 \in (x^4,y^4,z^4)^* in K[x,y,z]/(x^7+y^7-z^7) holds for infinitely many but not for almost all prime characteristics of the field K. This proves that tight closure exhibits a strong dependence on the arithmetic of the prime characteristic. The ideal (x,y,z) \subset K[x,y,z,u,v,w]/(x^7+y^7-z^7, ux^4+vy^4+wz^4+x^3y^3) has then the property that the cohomological dimension fluctuates arithmetically between 0 and 1. | |
| dc.identifier | https://arxiv.org/abs/math/0412033 | |
| dc.identifier | http://arxiv.org/abs/math/0412033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73453 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13A35; 11A41; 14H60 | |
| dc.title | On the arithmetic of tight closure | |
| dc.type | text |