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Overconvergent Modular Forms and the...

The University of Chicago.

Overconvergent Modular Forms and the P-Adic Jacquet-Langlands Correspondence.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Overconvergent Modular Forms and the P-Adic Jacquet-Langlands Correspondence./
Author:	Howe, Sean.
Description:	1 online resource (97 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:	9780355075199

Overconvergent Modular Forms and the P-Adic Jacquet-Langlands Correspondence.
Howe, Sean.

Overconvergent Modular Forms and the P-Adic Jacquet-Langlands Correspondence. - 1 online resource (97 pages)

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

Thesis (Ph.D.)

Includes bibliographical references

We construct a global p-adic Jacquet-Langlands transfer from overconvergent modular forms to naive p-adic automorphic forms on the quaternion algebra over Q ramified at p and infinity, answering an old question of Serre [26, paragraph (26)]. Using this transfer, we show that the completed Hecke algebra of naive automorphic forms on the quaternion algebra is isomorphic to the completed Hecke algebra of modular forms, and, conditional on a local-global compatibility conjecture, obtain new information about the local p-adic Jacquet- Langlands correspondence of Knight and Scholze. The construction and proofs live entirely in the world of p-adic geometry; in particular we do not use the smooth Jacquet-Langlands correspondence as an input.

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

Mode of access: World Wide Web

ISBN: 9780355075199Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Overconvergent Modular Forms and the P-Adic Jacquet-Langlands Correspondence.
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035 $a AAI10258387
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Howe, Sean. $3 1180610
245 1 0 $a Overconvergent Modular Forms and the P-Adic Jacquet-Langlands Correspondence.
264 0 $c 2017
300 $a 1 online resource (97 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: Matt Emerton.
502 $a Thesis (Ph.D.) $c The University of Chicago $d 2017.
504 $a Includes bibliographical references
520 $a We construct a global p-adic Jacquet-Langlands transfer from overconvergent modular forms to naive p-adic automorphic forms on the quaternion algebra over Q ramified at p and infinity, answering an old question of Serre [26, paragraph (26)]. Using this transfer, we show that the completed Hecke algebra of naive automorphic forms on the quaternion algebra is isomorphic to the completed Hecke algebra of modular forms, and, conditional on a local-global compatibility conjecture, obtain new information about the local p-adic Jacquet- Langlands correspondence of Knight and Scholze. The construction and proofs live entirely in the world of p-adic geometry; in particular we do not use the smooth Jacquet-Langlands correspondence as an input.
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 The University of Chicago. $b Mathematics. $3 1180611
773 0 $t Dissertation Abstracts International $g 78-11B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10258387 $z click for full text (PQDT)

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