Level Compatibility in the Passage from Modular Symbols to Cup Products
| dc.contributor.advisor | Sharifi, Romyar | en |
| dc.contributor.author | Williams, Ronnie Scott | |
| dc.creator | Williams, Ronnie Scott | en |
| dc.date.accessioned | 2016-12-09T20:32:02Z | |
| dc.date.available | 2016-12-09T20:32:02Z | |
| dc.date.issued | 2016 | |
| dc.identifier.uri | http://hdl.handle.net/10150/621579 | |
| dc.description.abstract | For a positive integer 𝛭 and an odd prime p, Sharifi defined a map 𝜛M from the first homology group of the modular curve Xโ(𝛭) with Zโ-coefficients to a second Galois cohomology group over โ(µM) with restricted ramification and Zโ(2)-coefficients that takes Manin symbols to certain cup products of cyclotomic 𝛭-units. Fukaya and Kato showed that if p|𝛭 and p ≥ 5, then 𝜛Mโ and 𝜛M are compatible via the map of homology induced by the quotient Xโ(𝛭p) -> Xโ (𝛭) and corestriction from โ(µMโ) to โ(µM). We show that for a prime 𝓁โค𝛭,𝓁≠p ≥ 5, the maps 𝜛M𝓁 and 𝜛M are again compatible under a certain combination of the two standard degeneracy maps from level 𝛭𝓁 to level 𝛭 and corestriction. | |
| dc.language.iso | en_US | en |
| dc.publisher | The University of Arizona. | en |
| dc.rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. | en |
| dc.subject | Mathematics | en |
| dc.title | Level Compatibility in the Passage from Modular Symbols to Cup Products | en_US |
| dc.type | text | en |
| dc.type | Electronic Dissertation | en |
| thesis.degree.grantor | University of Arizona | en |
| thesis.degree.level | doctoral | en |
| dc.contributor.committeemember | Sharifi, Romyar | en |
| dc.contributor.committeemember | Cais, Bryden | en |
| dc.contributor.committeemember | McCallum, William | en |
| dc.contributor.committeemember | Tiep, Pham Huu | en |
| thesis.degree.discipline | Graduate College | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.name | Ph.D. | en |
| refterms.dateFOA | 2018-08-20T15:36:51Z | |
| html.description.abstract | For a positive integer 𝛭 and an odd prime p, Sharifi defined a map 𝜛M from the first homology group of the modular curve Xโ(𝛭) with Zโ-coefficients to a second Galois cohomology group over โ(µM) with restricted ramification and Zโ(2)-coefficients that takes Manin symbols to certain cup products of cyclotomic 𝛭-units. Fukaya and Kato showed that if p|𝛭 and p ≥ 5, then 𝜛Mโ and 𝜛M are compatible via the map of homology induced by the quotient Xโ(𝛭p) -> Xโ (𝛭) and corestriction from โ(µMโ) to โ(µM). We show that for a prime 𝓁โค𝛭,𝓁≠p ≥ 5, the maps 𝜛M𝓁 and 𝜛M are again compatible under a certain combination of the two standard degeneracy maps from level 𝛭𝓁 to level 𝛭 and corestriction. |
