Geodesic
Non-Exactness of Direct Products of Quasi-Coherent Sheaves
Documenta mathematica, Tome 24 (2019), pp. 2037-2056
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

For a noetherian scheme that has an ample family of invertible sheaves, we prove that direct products in the category of quasi-coherent sheaves are not exact unless the scheme is affine. This result can especially be applied to all quasi-projective schemes over commutative noetherian rings. The main tools of the proof are the Gabriel-Popescu embedding and Roos' characterization of Grothendieck categories satisfying Ab6 and Ab4*.
DOI : 10.4171/dm/720
Classification : 13C60, 16D90, 16W50, 18E20
Mots-clés : quasi-coherent sheaf, Grothendieck category, divisorial scheme, invertible sheaf, direct product, Gabriel-Popescu embedding 
@article{10_4171_dm_720,
     author = {Ryo Kanda},
     title = {Non-Exactness of {Direct} {Products} of {Quasi-Coherent} {Sheaves}},
     journal = {Documenta mathematica},
     pages = {2037--2056},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/720},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/720/}
}
TY  - JOUR
AU  - Ryo Kanda
TI  - Non-Exactness of Direct Products of Quasi-Coherent Sheaves
JO  - Documenta mathematica
PY  - 2019
SP  - 2037
EP  - 2056
VL  - 24
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/720/
DO  - 10.4171/dm/720
ID  - 10_4171_dm_720
ER  - 
%0 Journal Article
%A Ryo Kanda
%T Non-Exactness of Direct Products of Quasi-Coherent Sheaves
%J Documenta mathematica
%D 2019
%P 2037-2056
%V 24
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/720/
%R 10.4171/dm/720
%F 10_4171_dm_720
Ryo Kanda. Non-Exactness of Direct Products of Quasi-Coherent Sheaves. Documenta mathematica, Tome 24 (2019), pp. 2037-2056. doi: 10.4171/dm/720

Cité par Sources :