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La réalisation étale et les opérations de Grothendieck


Ayoub, J (2014). La réalisation étale et les opérations de Grothendieck. Annales Scientifiques de l'Ecole Normale Superieure, 47(1):1-145.

Abstract

In this article, we construct étale realization functors defined on the categories DAét(X, Λ) of étale motives (without transfers) over a scheme X. Our construction is natural and relies on a relative rigidity theorem à la Suslin-Voevodsky that we will establish first. Then, we show that these realization functors are compatible with Grothendieck operations and the "nearby cycles" functors. Along the way, we prove a number of properties concerning étale motives.

Abstract

In this article, we construct étale realization functors defined on the categories DAét(X, Λ) of étale motives (without transfers) over a scheme X. Our construction is natural and relies on a relative rigidity theorem à la Suslin-Voevodsky that we will establish first. Then, we show that these realization functors are compatible with Grothendieck operations and the "nearby cycles" functors. Along the way, we prove a number of properties concerning étale motives.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Language:English
Date:February 2014
Deposited On:24 Sep 2014 15:01
Last Modified:30 Jul 2020 14:09
Publisher:Elsevier
ISSN:0012-9593
OA Status:Green
Publisher DOI:https://doi.org/10.24033/asens.2210
Related URLs:http://smf4.emath.fr/en/Publications/AnnalesENS/4_47/html/ens_ann-sc_47_1-145.php (Publisher)

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