Galois Deformation Theory for Norm Fields and its Arithmetic Applications.
dc.contributor.author | Kim, Wansu | en_US |
dc.date.accessioned | 2009-09-03T14:57:14Z | |
dc.date.available | NO_RESTRICTION | en_US |
dc.date.available | 2009-09-03T14:57:14Z | |
dc.date.issued | 2009 | en_US |
dc.date.submitted | 2009 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/63878 | |
dc.description.abstract | Let K be a finite extension of Q_p, and choose a uniformizer pi in K. Choose pi_{n+1} such that pi_1:=pi and pi_{n+1}^p=pi_n, and let K_infty denote the field extension of K obtained by adjoining pi_{n+1} for all n. We introduce a new technique using restriction to Gal(Kbar/K_infty) to study deformations and mod p reductions in p-adic Hodge theory. One of our main results in deformation theory is the existence of deformation rings for Gal(Kbar/K_infty)-representations "of height <= h" for any positive integer h, and we analyze their local structure. Using these Gal(Kbar/K_infty)-deformation rings, we give a different proof of Kisin's connected component analysis of flat deformation rings of a certain fixed Hodge type, which we used to prove the modularity of potentially Barsotti-Tate representations. This new proof works ``more uniformly'' for $p=2$, and does not use Zink's theory of windows and displays. We also study the equi-characteristic analogue of crystalline representations in the sense of Genestier-Lafforgue and Hartl. We show the full faithfulness of a natural functor from semilinear algebra objects, so-called local shtukas, into representations of the absolute Galois group of a local field of characteristic p>0. We also obtain equi-characteristic deformation rings for Galois representations that come from local shtukas, and study their local structure. | en_US |
dc.format.extent | 1874400 bytes | |
dc.format.extent | 1373 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | en_US |
dc.subject | Galois Deformation Theory and P-adic Hodge Theory | en_US |
dc.subject | Function Field Arithmetic and Local Shtukas | en_US |
dc.subject | Norm Fields | en_US |
dc.title | Galois Deformation Theory for Norm Fields and its Arithmetic Applications. | en_US |
dc.type | Thesis | en_US |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Mathematics | en_US |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | en_US |
dc.contributor.committeemember | Conrad, Brian D. | en_US |
dc.contributor.committeemember | Debacker, Stephen M. | en_US |
dc.contributor.committeemember | Boneh, Dan | en_US |
dc.contributor.committeemember | Lagarias, Jeffrey C. | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/63878/1/wansukim_1.pdf | |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
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