The conjectures of Artin-Tate and Birch-Swinnerton-Dyer

نویسندگان

چکیده

We provide two proofs that the conjecture of Artin-Tate for a fibered surface is equivalent to Birch-Swinnerton-Dyer Jacobian generic fibre. As byproduct, we obtain new proof theorem Geisser relating orders Brauer group and Tate-Shafarevich group.

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ژورنال

عنوان ژورنال: E?pijournal de ge?ome?trie alge?brique

سال: 2022

ISSN: ['2491-6765']

DOI: https://doi.org/10.46298/epiga.2022.7482