Geodesic
Differential forms in positive characteristic avoiding resolution of singularities
[Formes différentielles en caractéristique positive en évitant la résolution de singularités]
Huber, Annette1 ; Kebekus, Stefan2 ; Kelly, Shane1
1 Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany
2 Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany and University of Strasbourg Institute for Advanced Study (USIAS), Strasbourg, France
Bulletin de la Société Mathématique de France, Tome 145 (2017) no. 2, pp. 305-343

Voir la notice de l'article provenant de la source Numdam

This paper studies several notions of sheaves of differential forms that are better behaved on singular varieties than Kähler differentials. Our main focus lies on varieties that are defined over fields of positive characteristic. We identify two promising notions: the sheafification with respect to the cdh-topology, and right Kan extension from the subcategory of smooth varieties to the category of all varieties. Our main results are that both are cdh-sheaves and agree with Kähler differentials on smooth varieties. They agree on all varieties under weak resolution of singularities.

A number of examples highlight the difficulties that arise with torsion forms and with alternative candiates.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.24033/bsmf.2739
Classification : 14F10, 14F20, 14J17, 14F40
Keywords: Differential forms, singularities, cdh-topology

Huber, Annette 1 ; Kebekus, Stefan 2 ; Kelly, Shane 1

1 Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany
2 Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany and University of Strasbourg Institute for Advanced Study (USIAS), Strasbourg, France 
@article{BSMF_2017__145_2_305_0,
     author = {Huber, Annette and Kebekus, Stefan and Kelly, Shane},
     title = {Differential forms in positive characteristic avoiding resolution of singularities},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {305--343},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {145},
     number = {2},
     year = {2017},
     doi = {10.24033/bsmf.2739},
     mrnumber = {3749788},
     zbl = {1401.14103},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.24033/bsmf.2739/}
}
TY  - JOUR
AU  - Huber, Annette
AU  - Kebekus, Stefan
AU  - Kelly, Shane
TI  - Differential forms in positive characteristic avoiding resolution of singularities
JO  - Bulletin de la Société Mathématique de France
PY  - 2017
SP  - 305
EP  - 343
VL  - 145
IS  - 2
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/articles/10.24033/bsmf.2739/
DO  - 10.24033/bsmf.2739
LA  - en
ID  - BSMF_2017__145_2_305_0
ER  - 
%0 Journal Article
%A Huber, Annette
%A Kebekus, Stefan
%A Kelly, Shane
%T Differential forms in positive characteristic avoiding resolution of singularities
%J Bulletin de la Société Mathématique de France
%D 2017
%P 305-343
%V 145
%N 2
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/articles/10.24033/bsmf.2739/
%R 10.24033/bsmf.2739
%G en
%F BSMF_2017__145_2_305_0
Huber, Annette; Kebekus, Stefan; Kelly, Shane. Differential forms in positive characteristic avoiding resolution of singularities. Bulletin de la Société Mathématique de France, Tome 145 (2017) no. 2, pp. 305-343. doi: 10.24033/bsmf.2739

Cité par Sources :