The Hasse principle and the Brauer-Manin obstruction for curves

DOI10.1007/s00229-004-0502-9zbMath1069.11023OpenAlexW2030404815MaRDI QIDQ706180

E. Victor Flynn

Publication date: 2 February 2005

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-004-0502-9

zbMATH Keywords

Jacobianrational pointscurvesHasse principleBrauer-Manin obstruction

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields for curves (14H25) Abelian varieties of dimension (> 1) (11G10) Jacobians, Prym varieties (14H40) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

Related Items (14)

Galois sections for abelianized fundamental groups ⋮ Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\) ⋮ The Korteweg-de Vries equation and a Diophantine problem related to Bernoulli polynomials ⋮ Brauer-Manin obstructions on hyperelliptic curves ⋮ Failure of the Hasse principle for Enriques surfaces ⋮ Computing integral points on hyperelliptic curves using quadratic Chabauty ⋮ Five squares in arithmetic progression over quadratic fields ⋮ Rational points on curves ⋮ The Brauer-Manin obstruction for sections of the fundamental group ⋮ The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields ⋮ Rational classes and divisors on curves of genus 2 ⋮ On polyquadratic twists of \(X_0(N)\) ⋮ The \(d\)-primary Brauer-Manin obstruction for curves ⋮ Rational points on twisted modular curves

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some varieties with points only in a field extension
• On the method of Coleman and Chabauty
• Some interesting curves of genus 2 to 7
• Finding rational points on bielliptic genus 2 curves
• The Cassels-Tate pairing on polarized Abelian varieties
• ON ℚ-DERIVED POLYNOMIALS
• Covering collections and a challenge problem of Serre
• Implementing 2-descent for Jacobians of hyperelliptic curves
• The Hasse Principle modulo nth powers
• Canonical heights on the Jacobians of curves of genus 2 and the infinite descent
• ON A SHIMURA CURVE THAT IS A COUNTEREXAMPLE TO THE HASSE PRINCIPLE
• Chabauty methods using elliptic curves
• Arithmetic of diagonal quartic surfaces, II
• On the height constant for curves of genus two, II
• On the height constant for curves of genus two
• Computing the BrauerManin obstructions
• An Explicit Theory of Heights
• On large Picard groups and the Hasse Principle for curves and K3 surfaces
• Towers of 2-covers of hyperelliptic curves
• The arithmetic of certain quartic curves

This page was built for publication: The Hasse principle and the Brauer-Manin obstruction for curves