Quadratic Chabauty and rational points II: generalised height functions on Selmer varieties
Dogra, N, Balakrishnan, J
Abstract
We give new instances where Chabauty–Kim sets can be proved to be finite, by developing a notion of “generalised height functions” on Selmer varieties. We also explain how to compute these generalised heights in terms of iterated integrals and give the 1st explicit nonabelian Chabauty result for a curve X/Q whose Jacobian has Mordell–Weil rank larger than its genus.\n\n
Topics & Concepts
MathematicsIterated functionRank (graph theory)Quadratic equationPure mathematicsJacobian matrix and determinantGenusCombinatoricsMathematical analysisGeometryBotanyApplied mathematicsBiologyAlgebraic Geometry and Number TheoryPolynomial and algebraic computationAdvanced Algebra and Geometry