Matthew Bisatt

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20172026

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math.NT2017

Explicit root numbers of abelian varieties

Matthew Bisatt

The Birch and Swinnerton-Dyer conjecture predicts that the parity of the algebraic rank of an abelian variety over a global field should be controlled by the expected sign of the f…

math.NT2017

On the Birch--Swinnerton-Dyer conjecture and Schur indices

Matthew Bisatt, Vladimir Dokchitser

For every odd prime $p$ , we exhibit families of irreducible Artin representations $τ$ with the property that for every elliptic curve $E$ the order of the zero of the twisted $L$ -f…

math.NT2017

Frobenius elements in Galois representations with SL_n image

Matthew Bisatt

Suppose we have a elliptic curve over a number field whose mod $l$ representation has image isomorphic to $S L_{2} (F_{l})$ . We present a method to determine Frobenius elements…