• Corpus ID: 119317703

On the Frey-Mazur conjecture over low genus curves

@article{Bakker2013OnTF,
  title={On the Frey-Mazur conjecture over low genus curves},
  author={Benjamin Bakker and Jacob Tsimerman},
  journal={arXiv: Algebraic Geometry},
  year={2013}
}
The Frey--Mazur conjecture states that an elliptic curve over $\mathbb{Q}$ is determined up to isogeny by its $p$-torsion Galois representation for $p\geq 17$. We study a geometric analog of this conjecture, and show that the map from isogeny classes of "fake elliptic curves"---abelian surfaces with quaternionic multiplication---to their $p$-torsion Galois representations is one-to-one over function fields of small genus complex curves for sufficiently large $p$ relative to the genus. 
Measures of irrationality for hypersurfaces of large degree
We study various measures of irrationality for hypersurfaces of large degree in projective space and other varieties. These include the least degree of a rational covering of projective space, and

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