Bounding Picard numbers of surfaces using p-adic cohomology
| dc.creator | Abbott, Timothy G. | |
| dc.creator | Kedlaya, Kiran S. | |
| dc.creator | Roe, David | |
| dc.date | 2006-01-20 | |
| dc.date | 2007-01-18 | |
| dc.date.accessioned | 2026-07-07T07:41:29Z | |
| dc.date.available | 2026-07-07T07:41:29Z | |
| dc.description | Motivated by an application to LDPC (low density parity check) algebraic geometry codes described by Voloch and Zarzar, we describe a computational procedure for establishing an upper bound on the arithmetic or geometric Picard number of a smooth projective surface over a finite field, by computing the Frobenius action on p-adic cohomology to a small degree of p-adic accuracy. We have implemented this procedure in Magma; using this implementation, we exhibit several examples, such as smooth quartics over F_2 and F_3 with arithmetic Picard number 1, and a smooth quintic over F_2 with geometric Picard number 1. We also produce some examples of smooth quartics with geometric Picard number 2, which by a construction of van Luijk also have trivial geometric automorphism group. | |
| dc.description | 34 pages; v2: refereed version, to appear in proceedings "Arithmetic, Geometry, and Coding Theory (AGCT-10)" | |
| dc.identifier | https://arxiv.org/abs/math/0601508 | |
| dc.identifier | http://arxiv.org/abs/math/0601508 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122127 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C22, 14F30 | |
| dc.title | Bounding Picard numbers of surfaces using p-adic cohomology | |
| dc.type | text |