Motivic Eilenberg-MacLane spaces
Identifieur interne : 000402 ( Main/Exploration ); précédent : 000401; suivant : 000403Motivic Eilenberg-MacLane spaces
Auteurs : Vladimir Voevodsky [États-Unis]Source :
- Publications mathématiques de l'IHÉS [ 0073-8301 ] ; 2010-11-01.
Abstract
Abstract: In this paper we construct symmetric powers in the motivic homotopy categories of morphisms and finite correspondences associated with f-admissible subcategories in the categories of schemes of finite type over a field. Using this construction we provide a description of the motivic Eilenberg-MacLane spaces representing motivic cohomology on some f-admissible categories including the category of semi-normal quasi-projective schemes and, over fields which admit resolution of singularities, on some admissible subcategories including the category of smooth schemes. This description is then used to give a complete computation of the algebra of bistable motivic cohomological operations on smooth schemes over fields of characteristic zero and to obtain partial results on unstable operations which are required for the proof of the Bloch-Kato conjecture.
Url:
DOI: 10.1007/s10240-010-0024-9
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 001528
- to stream Istex, to step Curation: 001528
- to stream Istex, to step Checkpoint: 000358
- to stream Main, to step Merge: 000402
- to stream Main, to step Curation: 000402
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Motivic Eilenberg-MacLane spaces</title>
<author><name sortKey="Voevodsky, Vladimir" sort="Voevodsky, Vladimir" uniqKey="Voevodsky V" first="Vladimir" last="Voevodsky">Vladimir Voevodsky</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:677C078EFBAB18AC28BA5DE1486C99ECE0853581</idno>
<date when="2010" year="2010">2010</date>
<idno type="doi">10.1007/s10240-010-0024-9</idno>
<idno type="url">https://api.istex.fr/document/677C078EFBAB18AC28BA5DE1486C99ECE0853581/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001528</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001528</idno>
<idno type="wicri:Area/Istex/Curation">001528</idno>
<idno type="wicri:Area/Istex/Checkpoint">000358</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000358</idno>
<idno type="wicri:doubleKey">0073-8301:2010:Voevodsky V:motivic:eilenberg:maclane</idno>
<idno type="wicri:Area/Main/Merge">000402</idno>
<idno type="wicri:Area/Main/Curation">000402</idno>
<idno type="wicri:Area/Main/Exploration">000402</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Motivic Eilenberg-MacLane spaces</title>
<author><name sortKey="Voevodsky, Vladimir" sort="Voevodsky, Vladimir" uniqKey="Voevodsky V" first="Vladimir" last="Voevodsky">Vladimir Voevodsky</name>
<affiliation wicri:level="2"><country xml:lang="fr">États-Unis</country>
<wicri:regionArea>School of Mathematics, Institute for Advanced Study, 08540, Princeton, NJ</wicri:regionArea>
<placeName><region type="state">New Jersey</region>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">États-Unis</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Publications mathématiques de l'IHÉS</title>
<title level="j" type="sub">de l' IHES</title>
<title level="j" type="abbrev">Publ.math.IHES</title>
<idno type="ISSN">0073-8301</idno>
<idno type="eISSN">1618-1913</idno>
<imprint><publisher>Springer-Verlag</publisher>
<pubPlace>Berlin/Heidelberg</pubPlace>
<date type="published" when="2010-11-01">2010-11-01</date>
<biblScope unit="volume">112</biblScope>
<biblScope unit="issue">1</biblScope>
<biblScope unit="page" from="1">1</biblScope>
<biblScope unit="page" to="99">99</biblScope>
</imprint>
<idno type="ISSN">0073-8301</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0073-8301</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Abstract: In this paper we construct symmetric powers in the motivic homotopy categories of morphisms and finite correspondences associated with f-admissible subcategories in the categories of schemes of finite type over a field. Using this construction we provide a description of the motivic Eilenberg-MacLane spaces representing motivic cohomology on some f-admissible categories including the category of semi-normal quasi-projective schemes and, over fields which admit resolution of singularities, on some admissible subcategories including the category of smooth schemes. This description is then used to give a complete computation of the algebra of bistable motivic cohomological operations on smooth schemes over fields of characteristic zero and to obtain partial results on unstable operations which are required for the proof of the Bloch-Kato conjecture.</div>
</front>
</TEI>
<affiliations><list><country><li>États-Unis</li>
</country>
<region><li>New Jersey</li>
</region>
</list>
<tree><country name="États-Unis"><region name="New Jersey"><name sortKey="Voevodsky, Vladimir" sort="Voevodsky, Vladimir" uniqKey="Voevodsky V" first="Vladimir" last="Voevodsky">Vladimir Voevodsky</name>
</region>
<name sortKey="Voevodsky, Vladimir" sort="Voevodsky, Vladimir" uniqKey="Voevodsky V" first="Vladimir" last="Voevodsky">Vladimir Voevodsky</name>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000402 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000402 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Main |étape= Exploration |type= RBID |clé= ISTEX:677C078EFBAB18AC28BA5DE1486C99ECE0853581 |texte= Motivic Eilenberg-MacLane spaces }}
This area was generated with Dilib version V0.6.33. |