An Arakelov theoretic proof of the equality of conductor and discriminant
Journal de Théorie des Nombres de Bordeaux, Tome 16 (2004) no. 2, pp. 423-427.

Nous donnons une preuve utilisant la théorie d’Arakelov de l’égalité du conducteur et du discriminant.

We give an Arakelov theoretic proof of the equality of conductor and discriminant.

@article{JTNB_2004__16_2_423_0,
     author = {\"Unver, Sinan},
     title = {An {Arakelov} theoretic proof of the equality of conductor and discriminant},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {423--427},
     publisher = {Universit\'e Bordeaux 1},
     volume = {16},
     number = {2},
     year = {2004},
     doi = {10.5802/jtnb.454},
     mrnumber = {2143562},
     zbl = {1078.14030},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/jtnb.454/}
}
TY  - JOUR
AU  - Ünver, Sinan
TI  - An Arakelov theoretic proof of the equality of conductor and discriminant
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 2004
DA  - 2004///
SP  - 423
EP  - 427
VL  - 16
IS  - 2
PB  - Université Bordeaux 1
UR  - http://archive.numdam.org/articles/10.5802/jtnb.454/
UR  - https://www.ams.org/mathscinet-getitem?mr=2143562
UR  - https://zbmath.org/?q=an%3A1078.14030
UR  - https://doi.org/10.5802/jtnb.454
DO  - 10.5802/jtnb.454
LA  - en
ID  - JTNB_2004__16_2_423_0
ER  - 
Ünver, Sinan. An Arakelov theoretic proof of the equality of conductor and discriminant. Journal de Théorie des Nombres de Bordeaux, Tome 16 (2004) no. 2, pp. 423-427. doi : 10.5802/jtnb.454. http://archive.numdam.org/articles/10.5802/jtnb.454/

[Bloch] S. Bloch, Cycles on arithmetic schemes and Euler characteristics of curves. Proc. of Sympos. Pure Math. 46 (1987) AMS, 421–450. | MR 927991 | Zbl 0654.14004

[CPT] T. Chinburg, G. Pappas, M.J. Taylor, -constants and Arakelov Euler characteristics. Preprint, (1999).

[Deligne] P. Deligne, Le déterminant de la cohomologie. Contemp. Math. 67 (1987), 93–177. | MR 902592 | Zbl 0629.14008

[Falt] G. Faltings, Calculus on arithmetic surfaces. Ann. Math. 119 (1984), 387–424. | MR 740897 | Zbl 0559.14005

[Fulton] W. Fulton, Intersection theory. Springer-Verlag, Berlin, 1984. | MR 732620 | Zbl 0541.14005

[G-S] H. Gillet, C. Soulé, An arithmetic Riemann-Roch theorem. Invent. Math. 110 (1992), 473–543. | MR 1189489 | Zbl 0777.14008

[M-B] L. Moret-Bailly, La formule de Noether pour les surfaces arithmétiques. Invent. Math. 98 (1989), 499–509. | MR 1022303 | Zbl 0727.14014

[Mumf] D. Mumford, Stability of projective varieties. Einseign. Math. 23 (1977), 39–100. | MR 450272 | Zbl 0363.14003

[Saito] T. Saito, Conductor, discriminant, and the Noether formula of arithmetic surfaces. Duke Math. J. 57 (1988), 151–173. | MR 952229 | Zbl 0657.14017

Cité par Sources :