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Galois Deformation Ring and Barsotti...

Harvard University.

Galois Deformation Ring and Barsotti-Tate Representations in the Relative Case.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Galois Deformation Ring and Barsotti-Tate Representations in the Relative Case./
Author:	Moon, Yong Suk.
Description:	1 online resource (105 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Contained By:	Dissertation Abstracts International78-12B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355031355

Galois Deformation Ring and Barsotti-Tate Representations in the Relative Case.
Moon, Yong Suk.

Galois Deformation Ring and Barsotti-Tate Representations in the Relative Case. - 1 online resource (105 pages)

Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.

Thesis (Ph.D.)--Harvard University, 2016.

Includes bibliographical references

In this thesis, we study finite locally free group schemes, Galois deformation rings, and Barsotti-Tate representations in the relative case. We show three independent but related results, assuming p > 2.

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

Mode of access: World Wide Web

ISBN: 9780355031355Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Galois Deformation Ring and Barsotti-Tate Representations in the Relative Case.
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035 $a AAI10633067
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Moon, Yong Suk. $3 1193034
245 1 0 $a Galois Deformation Ring and Barsotti-Tate Representations in the Relative Case.
264 0 $c 2016
300 $a 1 online resource (105 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: 78-12(E), Section: B.
500 $a Adviser: Mark Kisin.
502 $a Thesis (Ph.D.)--Harvard University, 2016.
504 $a Includes bibliographical references
520 $a In this thesis, we study finite locally free group schemes, Galois deformation rings, and Barsotti-Tate representations in the relative case. We show three independent but related results, assuming p > 2.
520 $a First, we give a simpler alternative proof of Breuil's result on classifying finite flat group schemes over the ring of integers of a p-adic field by certain Breuil modules. Second, we prove that the locus of potentially semi-stable representations of the absolute Galois group of a p-adic field K with a specified Hodge-Tate type and Galois type cuts out a closed subspace of the generic fiber of a given Galois deformation ring, without assuming that K /Qp is finite. This is an extension of the corresponding result of Kisin when K/ Qp is finite.
520 $a Third, we study the locus of Barsotti-Tate representations in the relative case, via analyzing certain extendability of p-divisible groups. We prove that when the ramification index is less than p -- 1, the locus of relative Barsotti-Tate representations cuts out a closed subspace of the generic fiber of a Galois deformation ring, if the base scheme is 2-dimensional satisfying some conditions. When the ramification index is greater than p -- 1, we show that such a result does not hold in general.
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 Harvard University. $b Mathematics. $3 1193029
773 0 $t Dissertation Abstracts International $g 78-12B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10633067 $z click for full text (PQDT)

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