Motifs et adjoints
Kahn, Bruno1
1 Université Pierre et Marie Curie, Paris, France
Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 77-128.

We show in many cases the existence of adjoints to extension of scalars on categories of motivic nature, in the framework of field extensions. This is to be contrastedwith themore classical situationwhere one dealswith a finite typemorphism of schemes. Among various applications, one is a construction of a “Tate–Šafarevič motive” attached to an abelian variety over a function field. We also deduce a possible approach to Bloch’s conjecture on surfaces, by reduction to curves.

Publié le :
DOI : 10.4171/RSMUP/139-2
Classification : 14, 18
Mots clés : Motifs, adjonctions, géométrie birationnelle
Kahn, Bruno 1

1 Université Pierre et Marie Curie, Paris, France 
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     title = {Motifs et adjoints},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {77--128},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
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     url = {http://archive.numdam.org/articles/10.4171/RSMUP/139-2/}
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Kahn, Bruno. Motifs et adjoints. Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 77-128. doi : 10.4171/RSMUP/139-2. http://archive.numdam.org/articles/10.4171/RSMUP/139-2/

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