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Ramified Lifts of Galois Representat...

Mullath Mohammed Sherief, Mohammedzuhair.

Ramified Lifts of Galois Representations and Dimension of Ordinary Deformation Rings.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Ramified Lifts of Galois Representations and Dimension of Ordinary Deformation Rings./
Author:	Mullath Mohammed Sherief, Mohammedzuhair.
Description:	1 online resource (60 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
Contained By:	Dissertation Abstracts International78-11B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355049039

Ramified Lifts of Galois Representations and Dimension of Ordinary Deformation Rings.
Mullath Mohammed Sherief, Mohammedzuhair.

Ramified Lifts of Galois Representations and Dimension of Ordinary Deformation Rings. - 1 online resource (60 pages)

Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

Let F be a totally real number field, k a finite field of characteristic p and rho: Gal(F/F) → GLn( k) a continuous Galois representation. Under some technical hypotheses on rho we extend the method of Khare and Ramakrishna of constructing ramified characteristic zero lifts of \rh from the setting of GL2 to GLn. As an application of this method we prove the existence of closed points x ∈ Spec(Rord[1/p]), on a certain nearly ordinary deformation ring Rord , such that Mazur's dimension conjecture is true locally at x. In the process we obtain examples of ordinary Galois representations rho: GF, S∪Q → GLn( O), where O is a finite extension of Zp, such that its adjoint Selmer group H1L ( GF, S∪Q, ad0, rho &otimes; Qp/Zp) is finite. We then determine the exact size of these Selmer groups in terms of the ramification index of the primes in the auxiliary set.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355049039Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Ramified Lifts of Galois Representations and Dimension of Ordinary Deformation Rings.
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035 $a (MiAaPQ)AAI10288745
035 $a (MiAaPQ)ucla:15740
035 $a AAI10288745
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Mullath Mohammed Sherief, Mohammedzuhair. $3 1180776
245 1 0 $a Ramified Lifts of Galois Representations and Dimension of Ordinary Deformation Rings.
264 0 $c 2017
300 $a 1 online resource (60 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
500 $a Adviser: Chandrashekhar Khare.
502 $a Thesis (Ph.D.) $c University of California, Los Angeles $d 2017.
504 $a Includes bibliographical references
520 $a Let F be a totally real number field, k a finite field of characteristic p and rho: Gal(F/F) → GLn( k) a continuous Galois representation. Under some technical hypotheses on rho we extend the method of Khare and Ramakrishna of constructing ramified characteristic zero lifts of \rh from the setting of GL2 to GLn. As an application of this method we prove the existence of closed points x ∈ Spec(Rord[1/p]), on a certain nearly ordinary deformation ring Rord , such that Mazur's dimension conjecture is true locally at x. In the process we obtain examples of ordinary Galois representations rho: GF, S∪Q → GLn( O), where O is a finite extension of Zp, such that its adjoint Selmer group H1L ( GF, S∪Q, ad0, rho &otimes; Qp/Zp) is finite. We then determine the exact size of these Selmer groups in terms of the ramification index of the primes in the auxiliary set.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $3 1180777
773 0 $t Dissertation Abstracts International $g 78-11B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10288745 $z click for full text (PQDT)

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