We give an Arakelov theoretic proof of the equality of conductor and discriminant.
Nous donnons une preuve utilisant la théorie d’Arakelov de l’égalité du conducteur et du discriminant.
@article{JTNB_2004__16_2_423_0, author = {Sinan \"Unver}, 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 = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.454/} }
TY - JOUR AU - Sinan Ünver TI - An Arakelov theoretic proof of the equality of conductor and discriminant JO - Journal de théorie des nombres de Bordeaux PY - 2004 SP - 423 EP - 427 VL - 16 IS - 2 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.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 -
Sinan Ünver. An Arakelov theoretic proof of the equality of conductor and discriminant. Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 2, pp. 423-427. doi : 10.5802/jtnb.454. https://jtnb.centre-mersenne.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 | Zbl
[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 | Zbl
[Falt] G. Faltings, Calculus on arithmetic surfaces. Ann. Math. 119 (1984), 387–424. | MR | Zbl
[Fulton] W. Fulton, Intersection theory. Springer-Verlag, Berlin, 1984. | MR | Zbl
[G-S] H. Gillet, C. Soulé, An arithmetic Riemann-Roch theorem. Invent. Math. 110 (1992), 473–543. | MR | Zbl
[M-B] L. Moret-Bailly, La formule de Noether pour les surfaces arithmétiques. Invent. Math. 98 (1989), 499–509. | MR | Zbl
[Mumf] D. Mumford, Stability of projective varieties. Einseign. Math. 23 (1977), 39–100. | MR | Zbl
[Saito] T. Saito, Conductor, discriminant, and the Noether formula of arithmetic surfaces. Duke Math. J. 57 (1988), 151–173. | MR | Zbl
Cited by Sources: