For a positive integer ๐ญ and an odd prime p, Sharifi defined a map ๐M from the first homology group of the modular curve Xโ(๐ญ) with Zโ-coefficients to a second Galois cohomology group over โ(ยตM) with restricted ramification and Zโ(2)-coefficients that takes Manin symbols to certain cup products of cyclotomic ๐ญ-units. Fukaya and Kato showed that if p|๐ญ and p โฅ 5, then ๐Mโ and ๐M are compatible via the map of homology induced by the quotient Xโ(๐ญp) -> Xโ (๐ญ) and corestriction from โ(ยตMโ) to โ(ยตM). We show that for a prime ๐โค๐ญ,๐โ p โฅ 5, the maps ๐M๐ and ๐M are again compatible under a certain combination of the two standard degeneracy maps from level ๐ญ๐ to level ๐ญ and corestriction.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/621579 |
| Date | January 2016 |
| Creators | Williams, Ronnie Scott, Williams, Ronnie Scott |
| Contributors | Sharifi, Romyar, Sharifi, Romyar, Cais, Bryden, McCallum, William, Tiep, Pham Huu |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Electronic Dissertation |
| Rights | Copyright ยฉ 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. |
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