Ramification theory for varieties over a local field
Kato, Kazuya1 ; Saito, Takeshi2
1 Department of Mathematics, University of Chicago Chicago, IL, 60637 USA
2 Department of Mathematical Sciences, University of Tokyo Tokyo, 153-8914 Japan
Publications Mathématiques de l'IHÉS, Tome 117 (2013), pp. 1-178.

Voir la notice de l'article dans Numdam

We define generalizations of classical invariants of wild ramification for coverings on a variety of arbitrary dimension over a local field. For an ℓ-adic sheaf, we define its Swan class as a 0-cycle class supported on the wild ramification locus. We prove a formula of Riemann-Roch type for the Swan conductor of cohomology together with its relative version, assuming that the local field is of mixed characteristic.

We also prove the integrality of the Swan class for curves over a local field as a generalization of the Hasse-Arf theorem. We derive a proof of a conjecture of Serre on the Artin character for a group action with an isolated fixed point on a regular local ring, assuming the dimension is 2.

DOI : 10.1007/s10240-013-0048-z

Kato, Kazuya 1 ; Saito, Takeshi 2

1 Department of Mathematics, University of Chicago Chicago, IL, 60637 USA
2 Department of Mathematical Sciences, University of Tokyo Tokyo, 153-8914 Japan 
@article{PMIHES_2013__117__1_0,
     author = {Kato, Kazuya and Saito, Takeshi},
     title = {Ramification theory for varieties over a local field},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {1--178},
     publisher = {Springer-Verlag},
     volume = {117},
     year = {2013},
     doi = {10.1007/s10240-013-0048-z},
     zbl = {1290.14011},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10240-013-0048-z/}
}
TY  - JOUR
AU  - Kato, Kazuya
AU  - Saito, Takeshi
TI  - Ramification theory for varieties over a local field
JO  - Publications Mathématiques de l'IHÉS
PY  - 2013
SP  - 1
EP  - 178
VL  - 117
PB  - Springer-Verlag
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10240-013-0048-z/
DO  - 10.1007/s10240-013-0048-z
LA  - en
ID  - PMIHES_2013__117__1_0
ER  - 
%0 Journal Article
%A Kato, Kazuya
%A Saito, Takeshi
%T Ramification theory for varieties over a local field
%J Publications Mathématiques de l'IHÉS
%D 2013
%P 1-178
%V 117
%I Springer-Verlag
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10240-013-0048-z/
%R 10.1007/s10240-013-0048-z
%G en
%F PMIHES_2013__117__1_0
Kato, Kazuya; Saito, Takeshi. Ramification theory for varieties over a local field. Publications Mathématiques de l'IHÉS, Tome 117 (2013), pp. 1-178. doi : 10.1007/s10240-013-0048-z. https://geodesic-test.mathdoc.fr/articles/10.1007/s10240-013-0048-z/

Cité par Sources :