K -Theory and Intersection Theory
Identifieur interne : 000C69 ( Main/Exploration ); précédent : 000C68; suivant : 000C70K -Theory and Intersection Theory
Auteurs : Henri Gillet [États-Unis]Source :
Abstract
Abstract: The problem of defining intersection products on the Chow groups of schemes has a long history. Perhaps the first example of a theorem in intersection theory is Bézout’s theorem, which tells us that two projective plane curves C and D, of degrees c and d and which have no components in common, meet in at most cd points. Furthermore if one counts the points of C ∩ D with multiplicity, there are exactly cd points. Bezout’s theorem can be extended to closed subvarieties Y and Z of projective space over a field k, ℙ k n , with dim(Y) + dim(Z) = n and for which Y ∩ Z consists of a finite number of points.
Url:
DOI: 10.1007/978-3-540-27855-9_7
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 001471
- to stream Istex, to step Curation: 001471
- to stream Istex, to step Checkpoint: 000C05
- to stream Main, to step Merge: 000C79
- to stream Main, to step Curation: 000C69
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">K -Theory and Intersection Theory</title><author><name sortKey="Gillet, Henri" sort="Gillet, Henri" uniqKey="Gillet H" first="Henri" last="Gillet">Henri Gillet</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:64A7235462B8EDEE056837DC6ED743FA5992A969</idno><date when="2005" year="2005">2005</date><idno type="doi">10.1007/978-3-540-27855-9_7</idno><idno type="url">https://api.istex.fr/document/64A7235462B8EDEE056837DC6ED743FA5992A969/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001471</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001471</idno><idno type="wicri:Area/Istex/Curation">001471</idno><idno type="wicri:Area/Istex/Checkpoint">000C05</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000C05</idno><idno type="wicri:Area/Main/Merge">000C79</idno><idno type="wicri:Area/Main/Curation">000C69</idno><idno type="wicri:Area/Main/Exploration">000C69</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">K -Theory and Intersection Theory</title><author><name sortKey="Gillet, Henri" sort="Gillet, Henri" uniqKey="Gillet H" first="Henri" last="Gillet">Henri Gillet</name><affiliation wicri:level="4"><country xml:lang="fr">États-Unis</country><wicri:regionArea>Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249), 60607-7045, Chicago, IL</wicri:regionArea><placeName><region type="state">Illinois</region><settlement type="city">Chicago</settlement></placeName><orgName type="university">Université de l'Illinois à Chicago</orgName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">États-Unis</country></affiliation></author></analytic><monogr></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The problem of defining intersection products on the Chow groups of schemes has a long history. Perhaps the first example of a theorem in intersection theory is Bézout’s theorem, which tells us that two projective plane curves C and D, of degrees c and d and which have no components in common, meet in at most cd points. Furthermore if one counts the points of C ∩ D with multiplicity, there are exactly cd points. Bezout’s theorem can be extended to closed subvarieties Y and Z of projective space over a field k, ℙ k n , with dim(Y) + dim(Z) = n and for which Y ∩ Z consists of a finite number of points.</div></front></TEI><affiliations><list><country><li>États-Unis</li></country><region><li>Illinois</li></region><settlement><li>Chicago</li></settlement><orgName><li>Université de l'Illinois à Chicago</li></orgName></list><tree><country name="États-Unis"><region name="Illinois"><name sortKey="Gillet, Henri" sort="Gillet, Henri" uniqKey="Gillet H" first="Henri" last="Gillet">Henri Gillet</name></region><name sortKey="Gillet, Henri" sort="Gillet, Henri" uniqKey="Gillet H" first="Henri" last="Gillet">Henri Gillet</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 000C69 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000C69 | 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:64A7235462B8EDEE056837DC6ED743FA5992A969
|texte= K -Theory and Intersection Theory
}}
| This area was generated with Dilib version V0.6.33. |  |