Hecke’s Theorem on the Different for 3-Manifolds
[Théorème de Hecke sur les différente pour les 3-variétés]
Sawin, Will1  ; Shusterman, Mark2
1Princeton University, Fine Hall, 304 Washington Rd, Princeton NJ 08540 (USA)
2Faculty of Mathematics, And Computer Science, Weizmann Institute of Science, 234 Herzl Street, Rehovot 76100 (Israel)
Annales de l'Institut Fourier, Online first, 10 p.

Hecke has shown that the different of an extension of number fields is a square in the ideal class group. We prove an analog for branched covers of closed $3$-manifolds saying that the branch divisor is a square in the first homology group.

Hecke a montré que la différente d’une extension de corps de nombres est un carré dans le groupe des classes d’idéaux. Nous prouvons un analogue pour les revêtements ramifiés de $3$-variétés fermées en disant que le diviseur de ramification est un carré dans le premier groupe d’homologie.

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DOI : 10.5802/aif.3751
Classification : 57M27, 57M12, 11R29, 20J06, 55N10
Keywords: arithmetic topology, ramification divisor, hyperoctahedral group
Mots-clés : topologie arithmétique, diviseur de ramification, groupe hyperoctaédrique

Sawin, Will  1   ; Shusterman, Mark  2

1 Princeton University, Fine Hall, 304 Washington Rd, Princeton NJ 08540 (USA)
2 Faculty of Mathematics, And Computer Science, Weizmann Institute of Science, 234 Herzl Street, Rehovot 76100 (Israel) 
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Sawin, Will; Shusterman, Mark. Hecke’s Theorem on the Different for 3-Manifolds. Annales de l'Institut Fourier, Online first, 10 p.

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