Multivariable (φ,Γ)-modules and smooth o-torsion representations View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-04

AUTHORS

Gergely Zábrádi

ABSTRACT

Let G be a Qp-split reductive group with connected centre and Borel subgroup B=TN. We construct a right exact functor DΔ∨ from the category of smooth modulo pn representations of B to the category of projective limits of finitely generated étale (φ,Γ)-modules over a multivariable (indexed by the set of simple roots) commutative Laurent series ring. These correspond to representations of a direct power of Gal(Qp¯/Qp) via an equivalence of categories. Parabolic induction from a subgroup P=LPNP gives rise to a basechange from a Laurent series ring in those variables with corresponding simple roots contained in the Levi component LP. DΔ∨ is exact and yields finitely generated objects on the category SPA of finite length representations with subquotients of principal series as Jordan–Hölder factors. Lifting the functor DΔ∨ to all (noncommuting) variables indexed by the positive roots allows us to construct a G-equivariant sheaf Yπ,Δ on G / B and a G-equivariant continuous map from the Pontryagin dual π∨ of a smooth representation π of G to the global sections Yπ,Δ(G/B). We deduce that DΔ∨ is fully faithful on the full subcategory of SPA with Jordan–Hölder factors isomorphic to irreducible principal series. More... »

PAGES

935-995

Journal

TITLE

Selecta Mathematica

ISSUE

2

VOLUME

24

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00029-016-0259-5

DOI

http://dx.doi.org/10.1007/s00029-016-0259-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1028816617


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "name": [
            "Budapest, Hungary"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Z\u00e1br\u00e1di", 
        "givenName": "Gergely", 
        "id": "sg:person.014667031155.14", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014667031155.14"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s00209-016-1799-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011996602", 
          "https://doi.org/10.1007/s00209-016-1799-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00209-016-1799-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011996602", 
          "https://doi.org/10.1007/s00209-016-1799-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10240-013-0049-y", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021300175", 
          "https://doi.org/10.1007/s10240-013-0049-y"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jnt.2015.10.005", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025984638"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00039-007-0646-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030582894", 
          "https://doi.org/10.1007/s00039-007-0646-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1026191928449", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040830917", 
          "https://doi.org/10.1023/a:1026191928449"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/cbo9781107297524.008", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041762421"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s1474748003000021", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054938096"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0065-9266-2011-00623-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059337550"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1215/00127094-2916104", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064411452"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1215/00127094-3674441", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064411554"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2140/ant.2014.8.191", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069059116"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2140/ant.2015.9.2241", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069059201"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/mrl.2013.v20.n3.a1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072463092"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.24033/bsmf.2733", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1084646035"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2018-04", 
    "datePublishedReg": "2018-04-01", 
    "description": "Let G be a Qp-split reductive group with connected centre and Borel subgroup B=TN. We construct a right exact functor D\u0394\u2228 from the category of smooth modulo pn representations of B to the category of projective limits of finitely generated \u00e9tale (\u03c6,\u0393)-modules over a multivariable (indexed by the set of simple roots) commutative Laurent series ring. These correspond to representations of a direct power of Gal(Qp\u00af/Qp) via an equivalence of categories. Parabolic induction from a subgroup P=LPNP gives rise to a basechange from a Laurent series ring in those variables with corresponding simple roots contained in the Levi component LP. D\u0394\u2228 is exact and yields finitely generated objects on the category SPA of finite length representations with subquotients of principal series as Jordan\u2013H\u00f6lder factors. Lifting the functor D\u0394\u2228 to all (noncommuting) variables indexed by the positive roots allows us to construct a G-equivariant sheaf Y\u03c0,\u0394 on G / B and a G-equivariant continuous map from the Pontryagin dual \u03c0\u2228 of a smooth representation \u03c0 of G to the global sections Y\u03c0,\u0394(G/B). We deduce that D\u0394\u2228 is fully faithful on the full subcategory of SPA with Jordan\u2013H\u00f6lder factors isomorphic to irreducible principal series.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00029-016-0259-5", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1136551", 
        "issn": [
          "1022-1824", 
          "1420-9020"
        ], 
        "name": "Selecta Mathematica", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "24"
      }
    ], 
    "name": "Multivariable (\u03c6,\u0393)-modules and smooth o-torsion representations", 
    "pagination": "935-995", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "8946bc0594ccbb6a5d16a85dac19c21e386edee22b643693475bbdbad27494d1"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00029-016-0259-5"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1028816617"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00029-016-0259-5", 
      "https://app.dimensions.ai/details/publication/pub.1028816617"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T12:44", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000363_0000000363/records_70066_00000001.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs00029-016-0259-5"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00029-016-0259-5'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00029-016-0259-5'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00029-016-0259-5'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00029-016-0259-5'


 

This table displays all metadata directly associated to this object as RDF triples.

106 TRIPLES      21 PREDICATES      41 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00029-016-0259-5 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N62e290c749784259bdd3c8dd4ff932a2
4 schema:citation sg:pub.10.1007/s00039-007-0646-3
5 sg:pub.10.1007/s00209-016-1799-2
6 sg:pub.10.1007/s10240-013-0049-y
7 sg:pub.10.1023/a:1026191928449
8 https://doi.org/10.1016/j.jnt.2015.10.005
9 https://doi.org/10.1017/cbo9781107297524.008
10 https://doi.org/10.1017/s1474748003000021
11 https://doi.org/10.1090/s0065-9266-2011-00623-4
12 https://doi.org/10.1215/00127094-2916104
13 https://doi.org/10.1215/00127094-3674441
14 https://doi.org/10.2140/ant.2014.8.191
15 https://doi.org/10.2140/ant.2015.9.2241
16 https://doi.org/10.24033/bsmf.2733
17 https://doi.org/10.4310/mrl.2013.v20.n3.a1
18 schema:datePublished 2018-04
19 schema:datePublishedReg 2018-04-01
20 schema:description Let G be a Qp-split reductive group with connected centre and Borel subgroup B=TN. We construct a right exact functor DΔ∨ from the category of smooth modulo pn representations of B to the category of projective limits of finitely generated étale (φ,Γ)-modules over a multivariable (indexed by the set of simple roots) commutative Laurent series ring. These correspond to representations of a direct power of Gal(Qp¯/Qp) via an equivalence of categories. Parabolic induction from a subgroup P=LPNP gives rise to a basechange from a Laurent series ring in those variables with corresponding simple roots contained in the Levi component LP. DΔ∨ is exact and yields finitely generated objects on the category SPA of finite length representations with subquotients of principal series as Jordan–Hölder factors. Lifting the functor DΔ∨ to all (noncommuting) variables indexed by the positive roots allows us to construct a G-equivariant sheaf Yπ,Δ on G / B and a G-equivariant continuous map from the Pontryagin dual π∨ of a smooth representation π of G to the global sections Yπ,Δ(G/B). We deduce that DΔ∨ is fully faithful on the full subcategory of SPA with Jordan–Hölder factors isomorphic to irreducible principal series.
21 schema:genre research_article
22 schema:inLanguage en
23 schema:isAccessibleForFree true
24 schema:isPartOf N064836a9a5184a3bbd4d4180e07d8140
25 N192cc002e3834329be95922085390ef8
26 sg:journal.1136551
27 schema:name Multivariable (φ,Γ)-modules and smooth o-torsion representations
28 schema:pagination 935-995
29 schema:productId N36bf62aa920c4c0e9c2a8a36f504eb34
30 N478da06f2c9a4001a64f5474907c2572
31 Nb5e6301674bd4c34a5ec78cfecb097b2
32 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028816617
33 https://doi.org/10.1007/s00029-016-0259-5
34 schema:sdDatePublished 2019-04-11T12:44
35 schema:sdLicense https://scigraph.springernature.com/explorer/license/
36 schema:sdPublisher N0ae5ddeb811f42988c7134e61fb33e34
37 schema:url https://link.springer.com/10.1007%2Fs00029-016-0259-5
38 sgo:license sg:explorer/license/
39 sgo:sdDataset articles
40 rdf:type schema:ScholarlyArticle
41 N064836a9a5184a3bbd4d4180e07d8140 schema:issueNumber 2
42 rdf:type schema:PublicationIssue
43 N0ae5ddeb811f42988c7134e61fb33e34 schema:name Springer Nature - SN SciGraph project
44 rdf:type schema:Organization
45 N192cc002e3834329be95922085390ef8 schema:volumeNumber 24
46 rdf:type schema:PublicationVolume
47 N36bf62aa920c4c0e9c2a8a36f504eb34 schema:name dimensions_id
48 schema:value pub.1028816617
49 rdf:type schema:PropertyValue
50 N478da06f2c9a4001a64f5474907c2572 schema:name doi
51 schema:value 10.1007/s00029-016-0259-5
52 rdf:type schema:PropertyValue
53 N62e290c749784259bdd3c8dd4ff932a2 rdf:first sg:person.014667031155.14
54 rdf:rest rdf:nil
55 N754844733be04b8c909b079770db5a6a schema:name Budapest, Hungary
56 rdf:type schema:Organization
57 Nb5e6301674bd4c34a5ec78cfecb097b2 schema:name readcube_id
58 schema:value 8946bc0594ccbb6a5d16a85dac19c21e386edee22b643693475bbdbad27494d1
59 rdf:type schema:PropertyValue
60 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
61 schema:name Mathematical Sciences
62 rdf:type schema:DefinedTerm
63 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
64 schema:name Pure Mathematics
65 rdf:type schema:DefinedTerm
66 sg:journal.1136551 schema:issn 1022-1824
67 1420-9020
68 schema:name Selecta Mathematica
69 rdf:type schema:Periodical
70 sg:person.014667031155.14 schema:affiliation N754844733be04b8c909b079770db5a6a
71 schema:familyName Zábrádi
72 schema:givenName Gergely
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014667031155.14
74 rdf:type schema:Person
75 sg:pub.10.1007/s00039-007-0646-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030582894
76 https://doi.org/10.1007/s00039-007-0646-3
77 rdf:type schema:CreativeWork
78 sg:pub.10.1007/s00209-016-1799-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011996602
79 https://doi.org/10.1007/s00209-016-1799-2
80 rdf:type schema:CreativeWork
81 sg:pub.10.1007/s10240-013-0049-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1021300175
82 https://doi.org/10.1007/s10240-013-0049-y
83 rdf:type schema:CreativeWork
84 sg:pub.10.1023/a:1026191928449 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040830917
85 https://doi.org/10.1023/a:1026191928449
86 rdf:type schema:CreativeWork
87 https://doi.org/10.1016/j.jnt.2015.10.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025984638
88 rdf:type schema:CreativeWork
89 https://doi.org/10.1017/cbo9781107297524.008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041762421
90 rdf:type schema:CreativeWork
91 https://doi.org/10.1017/s1474748003000021 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054938096
92 rdf:type schema:CreativeWork
93 https://doi.org/10.1090/s0065-9266-2011-00623-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059337550
94 rdf:type schema:CreativeWork
95 https://doi.org/10.1215/00127094-2916104 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064411452
96 rdf:type schema:CreativeWork
97 https://doi.org/10.1215/00127094-3674441 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064411554
98 rdf:type schema:CreativeWork
99 https://doi.org/10.2140/ant.2014.8.191 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069059116
100 rdf:type schema:CreativeWork
101 https://doi.org/10.2140/ant.2015.9.2241 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069059201
102 rdf:type schema:CreativeWork
103 https://doi.org/10.24033/bsmf.2733 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084646035
104 rdf:type schema:CreativeWork
105 https://doi.org/10.4310/mrl.2013.v20.n3.a1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072463092
106 rdf:type schema:CreativeWork
 




Preview window. Press ESC to close (or click here)


...