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On 2-adic deformations
We compute the versal deformation ring of a split generic 2-dimensional representation χ 1 ⊕ χ 2 of the absolute Galois group of Q p . As an application, we show that the Breuil–Mézard conjecture for both non-split extensions of χ 1 by χ 2 and χ 2 by χ 1 implies the Breuil–Mézard conjecture for χ 1...
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| Published in: | Mathematische Zeitschrift 2017-08, Vol.286 (3-4), p.801-819 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c316t-f306c8b274b41c36b539770017e5e600057375dd25558e7ad1efcdf81487fd363 |
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| cites | cdi_FETCH-LOGICAL-c316t-f306c8b274b41c36b539770017e5e600057375dd25558e7ad1efcdf81487fd363 |
| container_end_page | 819 |
| container_issue | 3-4 |
| container_start_page | 801 |
| container_title | Mathematische Zeitschrift |
| container_volume | 286 |
| creator | Paškūnas, Vytautas |
| description | We compute the versal deformation ring of a split generic 2-dimensional representation
χ
1
⊕
χ
2
of the absolute Galois group of
Q
p
. As an application, we show that the Breuil–Mézard conjecture for both non-split extensions of
χ
1
by
χ
2
and
χ
2
by
χ
1
implies the Breuil–Mézard conjecture for
χ
1
⊕
χ
2
. The result is new for
p
=
2
, the proof works for all primes. |
| doi_str_mv | 10.1007/s00209-016-1785-8 |
| format | article |
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χ
1
⊕
χ
2
of the absolute Galois group of
Q
p
. As an application, we show that the Breuil–Mézard conjecture for both non-split extensions of
χ
1
by
χ
2
and
χ
2
by
χ
1
implies the Breuil–Mézard conjecture for
χ
1
⊕
χ
2
. The result is new for
p
=
2
, the proof works for all primes.</description><identifier>ISSN: 0025-5874</identifier><identifier>EISSN: 1432-1823</identifier><identifier>DOI: 10.1007/s00209-016-1785-8</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Deformation ; Mathematics ; Mathematics and Statistics ; Proving</subject><ispartof>Mathematische Zeitschrift, 2017-08, Vol.286 (3-4), p.801-819</ispartof><rights>Springer-Verlag Berlin Heidelberg 2016</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-f306c8b274b41c36b539770017e5e600057375dd25558e7ad1efcdf81487fd363</citedby><cites>FETCH-LOGICAL-c316t-f306c8b274b41c36b539770017e5e600057375dd25558e7ad1efcdf81487fd363</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Paškūnas, Vytautas</creatorcontrib><title>On 2-adic deformations</title><title>Mathematische Zeitschrift</title><addtitle>Math. Z</addtitle><description>We compute the versal deformation ring of a split generic 2-dimensional representation
χ
1
⊕
χ
2
of the absolute Galois group of
Q
p
. As an application, we show that the Breuil–Mézard conjecture for both non-split extensions of
χ
1
by
χ
2
and
χ
2
by
χ
1
implies the Breuil–Mézard conjecture for
χ
1
⊕
χ
2
. The result is new for
p
=
2
, the proof works for all primes.</description><subject>Deformation</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Proving</subject><issn>0025-5874</issn><issn>1432-1823</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1j7tPwzAQxi0EEqGwIrFVYjbc-XXOiCpeUqUuMFtJbKNUNCl2OvDf4yoMLOiGb_gepx9jNwh3CED3GUBAzQENR7Ka2xNWoZKCoxXylFXF1lxbUufsIuctQDFJVex6MywFb3zfLX2IY9o1Uz8O-ZKdxeYzh6tfXbD3p8e31Qtfb55fVw9r3kk0E48STGdbQapV2EnTalkTlXEKOhgA0CRJey-01jZQ4zHEzkeLylL00sgFu51392n8OoQ8ue14SEN56bAuJ2oFVFI4p7o05pxCdPvU75r07RDcEd_N-K7guyO-s6Uj5k4u2eEjpD_L_5Z-ALGvWWA</recordid><startdate>20170801</startdate><enddate>20170801</enddate><creator>Paškūnas, Vytautas</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170801</creationdate><title>On 2-adic deformations</title><author>Paškūnas, Vytautas</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-f306c8b274b41c36b539770017e5e600057375dd25558e7ad1efcdf81487fd363</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Deformation</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Proving</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Paškūnas, Vytautas</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematische Zeitschrift</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Paškūnas, Vytautas</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On 2-adic deformations</atitle><jtitle>Mathematische Zeitschrift</jtitle><stitle>Math. Z</stitle><date>2017-08-01</date><risdate>2017</risdate><volume>286</volume><issue>3-4</issue><spage>801</spage><epage>819</epage><pages>801-819</pages><issn>0025-5874</issn><eissn>1432-1823</eissn><abstract>We compute the versal deformation ring of a split generic 2-dimensional representation
χ
1
⊕
χ
2
of the absolute Galois group of
Q
p
. As an application, we show that the Breuil–Mézard conjecture for both non-split extensions of
χ
1
by
χ
2
and
χ
2
by
χ
1
implies the Breuil–Mézard conjecture for
χ
1
⊕
χ
2
. The result is new for
p
=
2
, the proof works for all primes.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00209-016-1785-8</doi><tpages>19</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0025-5874 |
| ispartof | Mathematische Zeitschrift, 2017-08, Vol.286 (3-4), p.801-819 |
| issn | 0025-5874 1432-1823 |
| language | eng |
| recordid | cdi_proquest_journals_1919129407 |
| source | Springer Nature:Jisc Collections:Springer Nature Read and Publish 2023-2025: Springer Reading List |
| subjects | Deformation Mathematics Mathematics and Statistics Proving |
| title | On 2-adic deformations |
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