The Drinfeld modular Jacobian J(1)(n) has connected fibers.
dc.contributor.author | Shastry, Sreekar M. | |
dc.contributor.advisor | Conrad, Brian D. | |
dc.date.accessioned | 2016-08-30T15:57:21Z | |
dc.date.available | 2016-08-30T15:57:21Z | |
dc.date.issued | 2005 | |
dc.identifier.uri | http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3192777 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/125499 | |
dc.description.abstract | We study the integral model of the Drinfeld modular curve <italic>X</italic><sub> 1</sub>(<italic>n</italic>) for a prime <italic>n</italic> ∈ <blkbd>Fq</blkbd> [<italic>T</italic>]. A function field analogue of the theory of Igusa curves is introduced to describe its reduction mod <italic>n</italic>. A result describing the universal deformation ring of a pair consisting of a supersingular Drinfeld module and a point of order <italic>n</italic> in terms of the Hasse invariant of that Drinfeld module is proved. We then apply Jung-Hirzebruch resolution for arithmetic surfaces to produce a regular model of <italic>X</italic><sub>1</sub>(<italic>n</italic>) which, after contractions in the special fiber, gives a regular model with geometrically integral fiber over <italic>n</italic>. Thus the mod <italic>n</italic> component group of <italic> J</italic><sub>1</sub>(<italic>n</italic>) is trivial, i.e. <italic>J</italic><sub> 1</sub>(<italic>n</italic>) has connected fibers. | |
dc.format.extent | 67 p. | |
dc.language | English | |
dc.language.iso | EN | |
dc.subject | Connected Fibers | |
dc.subject | Drinfeld Modular | |
dc.subject | Has | |
dc.subject | J1 | |
dc.subject | Jacobian | |
dc.subject | Number Theory | |
dc.title | The Drinfeld modular Jacobian J(1)(n) has connected fibers. | |
dc.type | Thesis | |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Mathematics | |
dc.description.thesisdegreediscipline | Pure Sciences | |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/125499/2/3192777.pdf | |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
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