Parity in Bloch’s conductor formula in even dimension
Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 2, pp. 403-421.

Pour une variété sur un corps local, Bloch a proposé une formule conjecturale pour la somme alternée du conducteur d’Artin de la cohomologie -adique. On démontre que la formule modulo 2 est vraie dans le cas où la dimension de la variété est paire.

For a variety over a local field, Bloch proposed a conjectural formula for the alternating sum of Artin conductor of -adic cohomology. We prove that the formula is valid modulo 2 if the variety has even dimension.

DOI : 10.5802/jtnb.453
Saito, Takeshi 1

1 Department of Mathematical Sciences, University of Tokyo Tokyo 153-8914 Japan
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Saito, Takeshi. Parity in Bloch’s conductor formula in even dimension. Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 2, pp. 403-421. doi : 10.5802/jtnb.453. http://archive.numdam.org/articles/10.5802/jtnb.453/

[1] S. Bloch, Cycles on arithmetic schemes and Euler characteristics of curves. Proc. Symp. Pure Math. AMS 46 Part 2 (1987), 421–450. | MR | Zbl

[2] —–, De Rham cohomology and conductors of curves. Duke Math. J. 54 (1987), 295–308. | Zbl

[3] P. Deligne (after A. Grothendieck), Résumé des premiers exposés de A.Grothendieck. in SGA7I, Lecture notes in Math. 288, Springer, 1–23. | Zbl

[4] A. Dold, D. Puppe, Homologie nicht additiver Funktoren. Ann. Inst. Fourier 11 (1961), 201–312. | Numdam | MR | Zbl

[5] K. Fujiwara, A proof of the absolute purity conjecture (after Gabber). Algebraic geometry 2000, Azumino (Hotaka), 153–183, Adv. Stud. Pure Math. 36, Math. Soc. Japan, Tokyo, 2002 | MR | Zbl

[6] W. Fulton, Intersection theory. Springer. | MR | Zbl

[7] L. Illusie, Complexe cotangent et déformations I. Lecture notes in Math. 239 Springer. | MR | Zbl

[8] K. Kato, T. Saito, Conductor formula of Bloch. To appear in Publ. Math. IHES. | Numdam | MR

[9] T. Ochiai, -independence of the trace of monodromy. Math. Ann. 315 (1999), 321–340. | MR | Zbl

[10] T. Saito, Self-intersection 0-cycles and coherent sheaves on arithmetic schemes. Duke Math. J. 57 (1988), 555–578. | MR | Zbl

[11] —–, Jacobi sum Hecke characters, de Rham discriminant, and the determinant of -adic cohomologies. J. of Alg. Geom. 3 (1994), 411–434. | Zbl

[12] J.-P. Serre, Conducteurs d’Artin des caracteres réels. Inventiones Math. 14 (1971), 173–183. | MR | Zbl

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