AN "ANTI-HASSE PRINCIPLE" FOR PRIME TWISTS

DOI10.1142/S1793042108001572zbMath1152.11025arXivmath/0609465OpenAlexW1988973434MaRDI QIDQ3526562

Pete L. Clark

Publication date: 25 September 2008

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609465

zbMATH Keywords

Shimura curvequadratic twistmodular curveAtkin-Lehner involutionlocal-global principles

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Arithmetic aspects of modular and Shimura varieties (11G18)

Related Items (8)

ABC and the Hasse principle for quadratic twists of hyperelliptic curves ⋮ Curves over every global field violating the local-global principle ⋮ Hasse principle violations in twist families of superelliptic curves ⋮ Rational points on Atkin-Lehner quotients of geometrically hyperelliptic Shimura curves ⋮ COMPUTING POINTS ON BIELLIPTIC MODULAR CURVES OVER FIXED QUADRATIC FIELDS ⋮ Hasse principle violations for Atkin-Lehner twists of Shimura curves ⋮ On polyquadratic twists of \(X_0(N)\) ⋮ Counterexamples to the local-global principle for non-singular plane curves and a cubic analogue of Ankeny-Artin-Chowla-Mordell conjecture

Cites Work

• Genus zero translates of three point ramified Galois extensions
• Bielliptic modular curves
• Q-Curves and Abelian Varieties of GL₂ -Type

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