By extending Kuga-Satake period morphisms to singular models, the authors prove the Tate conjecture for many geometric-genus-one surfaces and BSD for height-one elliptic curves over genus-one function fields.
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The Tate conjecture for surfaces of geometric genus one -- embracing singularities
By extending Kuga-Satake period morphisms to singular models, the authors prove the Tate conjecture for many geometric-genus-one surfaces and BSD for height-one elliptic curves over genus-one function fields.