Serveur d'exploration Bourbaki

Attention, ce site est en cours de développement !
Attention, site généré par des moyens informatiques à partir de corpus bruts.
Les informations ne sont donc pas validées.

Crystalline cohomology and GL(2, ℚ)

Identifieur interne : 001A59 ( Istex/Checkpoint ); précédent : 001A58; suivant : 001A60

Crystalline cohomology and GL(2, ℚ)

Auteurs : Gerd Faltings [États-Unis] ; Bruce W. Jordan [États-Unis]

Source :

RBID : ISTEX:3944615936504C09CDB8A0094DD69905C9EF510E

Descripteurs français

English descriptors

Abstract

Abstract: This paper applies recent advances in crystalline cohomology to the classical case of open elliptic modular curves. In so doing control is gained over the action of inertia in the Galois representations attached to modular forms. Our aim is to study the modular Galois representations attached to automorphic forms modp of weightk≥2. We generalize to higher weightk several results which were previously accessible only in the case of weight 2 where jacobian varieties can be invoked. Additionally we reconsider Gross’s theorem on companion forms in a crystalline context.

Url:
DOI: 10.1007/BF02783205


Affiliations:


Links toward previous steps (curation, corpus...)


Links to Exploration step

ISTEX:3944615936504C09CDB8A0094DD69905C9EF510E

Le document en format XML

<record>
<TEI wicri:istexFullTextTei="biblStruct">
<teiHeader>
<fileDesc>
<titleStmt>
<title xml:lang="en">Crystalline cohomology and GL(2, ℚ)</title>
<author>
<name sortKey="Faltings, Gerd" sort="Faltings, Gerd" uniqKey="Faltings G" first="Gerd" last="Faltings">Gerd Faltings</name>
</author>
<author>
<name sortKey="Jordan, Bruce W" sort="Jordan, Bruce W" uniqKey="Jordan B" first="Bruce W." last="Jordan">Bruce W. Jordan</name>
</author>
</titleStmt>
<publicationStmt>
<idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:3944615936504C09CDB8A0094DD69905C9EF510E</idno>
<date when="1995" year="1995">1995</date>
<idno type="doi">10.1007/BF02783205</idno>
<idno type="url">https://api.istex.fr/document/3944615936504C09CDB8A0094DD69905C9EF510E/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">000B79</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000B79</idno>
<idno type="wicri:Area/Istex/Curation">000B79</idno>
<idno type="wicri:Area/Istex/Checkpoint">001A59</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">001A59</idno>
</publicationStmt>
<sourceDesc>
<biblStruct>
<analytic>
<title level="a" type="main" xml:lang="en">Crystalline cohomology and GL(2, ℚ)</title>
<author>
<name sortKey="Faltings, Gerd" sort="Faltings, Gerd" uniqKey="Faltings G" first="Gerd" last="Faltings">Gerd Faltings</name>
<affiliation wicri:level="4">
<country xml:lang="fr">États-Unis</country>
<wicri:regionArea>Department of Mathematics, Princeton University, 08544, Princeton, NJ</wicri:regionArea>
<placeName>
<region type="state">New Jersey</region>
<settlement type="city">Princeton (New Jersey)</settlement>
</placeName>
<orgName type="university">Université de Princeton</orgName>
</affiliation>
</author>
<author>
<name sortKey="Jordan, Bruce W" sort="Jordan, Bruce W" uniqKey="Jordan B" first="Bruce W." last="Jordan">Bruce W. Jordan</name>
<affiliation wicri:level="2">
<country xml:lang="fr">États-Unis</country>
<wicri:regionArea>Department of Mathematics, Baruch College, CUNY, 17 Lexington Avenue, Box 509, 10010, New York, NY</wicri:regionArea>
<placeName>
<region type="state">État de New York</region>
</placeName>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series>
<title level="j">Israel Journal of Mathematics</title>
<title level="j" type="abbrev">Israel J. Math.</title>
<idno type="ISSN">0021-2172</idno>
<idno type="eISSN">1565-8511</idno>
<imprint>
<publisher>Springer-Verlag</publisher>
<pubPlace>New York</pubPlace>
<date type="published" when="1995-10-01">1995-10-01</date>
<biblScope unit="volume">90</biblScope>
<biblScope unit="issue">1-3</biblScope>
<biblScope unit="page" from="1">1</biblScope>
<biblScope unit="page" to="66">66</biblScope>
</imprint>
<idno type="ISSN">0021-2172</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt>
<idno type="ISSN">0021-2172</idno>
</seriesStmt>
</fileDesc>
<profileDesc>
<textClass>
<keywords scheme="KwdEn" xml:lang="en">
<term>Algebra</term>
<term>Cohomology</term>
<term>Cohomology class</term>
<term>Companion form</term>
<term>Companion forms</term>
<term>Comparison theorem</term>
<term>Cond</term>
<term>Constant coefficients</term>
<term>Constant term</term>
<term>Constant terms</term>
<term>Crystalline</term>
<term>Crystalline cohomology</term>
<term>Crystalline methods</term>
<term>Crystalline theory</term>
<term>Cusp</term>
<term>Cusp form</term>
<term>Cusp forms</term>
<term>Dirichlet</term>
<term>Dirichlet character</term>
<term>Dirichlet characters</term>
<term>Duality</term>
<term>Eigenvalue</term>
<term>Eisenstein</term>
<term>Eisenstein case</term>
<term>Eisenstein ideals</term>
<term>Eisenstein series</term>
<term>Elliptic</term>
<term>Elliptic curve</term>
<term>Elliptic curves</term>
<term>Exact order</term>
<term>Exact sequence</term>
<term>Faltings</term>
<term>Filtration</term>
<term>Finite extension</term>
<term>Frobenius</term>
<term>Frobenius element</term>
<term>Functional equation</term>
<term>Galois</term>
<term>Galois representations</term>
<term>Good reduction</term>
<term>Hecke</term>
<term>Hecke algebra</term>
<term>Hecke correspondence</term>
<term>Hecke correspondences</term>
<term>Hecke eigenvalues</term>
<term>Hecke operators</term>
<term>Higher weight</term>
<term>Inertia</term>
<term>Inertia subgroup</term>
<term>Inventiones mathematicae</term>
<term>Irreducible</term>
<term>Isogeny</term>
<term>Isomorphic</term>
<term>Isomorphism</term>
<term>Jordan</term>
<term>Local requirements</term>
<term>Math</term>
<term>Maximal</term>
<term>Maximal ideals</term>
<term>Modp</term>
<term>Modular</term>
<term>Modular form</term>
<term>Modular forms</term>
<term>Modular representations</term>
<term>Module</term>
<term>Modulo</term>
<term>Modulus</term>
<term>Multiplicative</term>
<term>Nebentypus character</term>
<term>Notation</term>
<term>Number theory</term>
<term>Ordinary locus</term>
<term>Other hand</term>
<term>Parametrized</term>
<term>Parametrized cusp</term>
<term>Positive integer</term>
<term>Power series</term>
<term>Primitive vector</term>
<term>Quotient</term>
<term>Ramified</term>
<term>Reducible</term>
<term>Residue field</term>
<term>Rham</term>
<term>Second factor</term>
<term>Serre</term>
<term>Serre duality</term>
<term>Sheaf</term>
<term>Simple poles</term>
<term>Special fiber</term>
<term>Subgroup</term>
<term>Symm</term>
<term>Tamely ramified</term>
<term>Tate curve</term>
<term>Universal elliptic curve</term>
<term>Unramified</term>
</keywords>
<keywords scheme="Teeft" xml:lang="en">
<term>Algebra</term>
<term>Cohomology</term>
<term>Cohomology class</term>
<term>Companion form</term>
<term>Companion forms</term>
<term>Comparison theorem</term>
<term>Cond</term>
<term>Constant coefficients</term>
<term>Constant term</term>
<term>Constant terms</term>
<term>Crystalline</term>
<term>Crystalline cohomology</term>
<term>Crystalline methods</term>
<term>Crystalline theory</term>
<term>Cusp</term>
<term>Cusp form</term>
<term>Cusp forms</term>
<term>Dirichlet</term>
<term>Dirichlet character</term>
<term>Dirichlet characters</term>
<term>Duality</term>
<term>Eigenvalue</term>
<term>Eisenstein</term>
<term>Eisenstein case</term>
<term>Eisenstein ideals</term>
<term>Eisenstein series</term>
<term>Elliptic</term>
<term>Elliptic curve</term>
<term>Elliptic curves</term>
<term>Exact order</term>
<term>Exact sequence</term>
<term>Faltings</term>
<term>Filtration</term>
<term>Finite extension</term>
<term>Frobenius</term>
<term>Frobenius element</term>
<term>Functional equation</term>
<term>Galois</term>
<term>Galois representations</term>
<term>Good reduction</term>
<term>Hecke</term>
<term>Hecke algebra</term>
<term>Hecke correspondence</term>
<term>Hecke correspondences</term>
<term>Hecke eigenvalues</term>
<term>Hecke operators</term>
<term>Higher weight</term>
<term>Inertia</term>
<term>Inertia subgroup</term>
<term>Inventiones mathematicae</term>
<term>Irreducible</term>
<term>Isogeny</term>
<term>Isomorphic</term>
<term>Isomorphism</term>
<term>Jordan</term>
<term>Local requirements</term>
<term>Math</term>
<term>Maximal</term>
<term>Maximal ideals</term>
<term>Modp</term>
<term>Modular</term>
<term>Modular form</term>
<term>Modular forms</term>
<term>Modular representations</term>
<term>Module</term>
<term>Modulo</term>
<term>Modulus</term>
<term>Multiplicative</term>
<term>Nebentypus character</term>
<term>Notation</term>
<term>Number theory</term>
<term>Ordinary locus</term>
<term>Other hand</term>
<term>Parametrized</term>
<term>Parametrized cusp</term>
<term>Positive integer</term>
<term>Power series</term>
<term>Primitive vector</term>
<term>Quotient</term>
<term>Ramified</term>
<term>Reducible</term>
<term>Residue field</term>
<term>Rham</term>
<term>Second factor</term>
<term>Serre</term>
<term>Serre duality</term>
<term>Sheaf</term>
<term>Simple poles</term>
<term>Special fiber</term>
<term>Subgroup</term>
<term>Symm</term>
<term>Tamely ramified</term>
<term>Tate curve</term>
<term>Universal elliptic curve</term>
<term>Unramified</term>
</keywords>
<keywords scheme="Wicri" type="geographic" xml:lang="fr">
<term>Jordanie</term>
</keywords>
</textClass>
<langUsage>
<language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front>
<div type="abstract" xml:lang="en">Abstract: This paper applies recent advances in crystalline cohomology to the classical case of open elliptic modular curves. In so doing control is gained over the action of inertia in the Galois representations attached to modular forms. Our aim is to study the modular Galois representations attached to automorphic forms modp of weightk≥2. We generalize to higher weightk several results which were previously accessible only in the case of weight 2 where jacobian varieties can be invoked. Additionally we reconsider Gross’s theorem on companion forms in a crystalline context.</div>
</front>
</TEI>
<affiliations>
<list>
<country>
<li>États-Unis</li>
</country>
<region>
<li>New Jersey</li>
<li>État de New York</li>
</region>
<settlement>
<li>Princeton (New Jersey)</li>
</settlement>
<orgName>
<li>Université de Princeton</li>
</orgName>
</list>
<tree>
<country name="États-Unis">
<region name="New Jersey">
<name sortKey="Faltings, Gerd" sort="Faltings, Gerd" uniqKey="Faltings G" first="Gerd" last="Faltings">Gerd Faltings</name>
</region>
<name sortKey="Jordan, Bruce W" sort="Jordan, Bruce W" uniqKey="Jordan B" first="Bruce W." last="Jordan">Bruce W. Jordan</name>
</country>
</tree>
</affiliations>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Istex/Checkpoint
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001A59 | SxmlIndent | more

Ou

HfdSelect -h $EXPLOR_AREA/Data/Istex/Checkpoint/biblio.hfd -nk 001A59 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Mathematiques
   |area=    BourbakiV1
   |flux=    Istex
   |étape=   Checkpoint
   |type=    RBID
   |clé=     ISTEX:3944615936504C09CDB8A0094DD69905C9EF510E
   |texte=   Crystalline cohomology and GL(2, ℚ)
}}

Wicri

This area was generated with Dilib version V0.6.33.
Data generation: Thu Jul 5 10:00:31 2018. Site generation: Sat Nov 19 17:42:07 2022