Geodesic
The conjectures of Artin-Tate and Birch-Swinnerton-Dyer
Épijournal de Géométrie Algébrique, Tome 6 (2022)

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We provide two proofs that the conjecture of Artin-Tate for a fibered surface is equivalent to the conjecture of Birch-Swinnerton-Dyer for the Jacobian of the generic fibre. As a byproduct, we obtain a new proof of a theorem of Geisser relating the orders of the Brauer group and the Tate-Shafarevich group.
DOI : 10.46298/epiga.2022.7482
Classification : 11G40 
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     author = {Lichtenbaum, S. and Ramachandran, N. and Suzuki, T.},
     title = {The conjectures of {Artin-Tate} and {Birch-Swinnerton-Dyer}},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     volume = {6},
     year = {2022},
     doi = {10.46298/epiga.2022.7482},
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Lichtenbaum, S.; Ramachandran, N.; Suzuki, T. The conjectures of Artin-Tate and Birch-Swinnerton-Dyer. Épijournal de Géométrie Algébrique, Tome 6 (2022). doi: 10.46298/epiga.2022.7482

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