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.

@article{JTNB_2004__16_2_403_0,
     author = {Saito, Takeshi},
     title = {Parity in Bloch{\textquoteright}s conductor formula in even dimension},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {403--421},
     publisher = {Universit\'e Bordeaux 1},
     volume = {16},
     number = {2},
     year = {2004},
     doi = {10.5802/jtnb.453},
     mrnumber = {2143561},
     zbl = {02188524},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jtnb.453/}
}
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://www.numdam.org/articles/10.5802/jtnb.453/

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