Results 41 to 50 of about 3,799,599 (344)
Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties [PDF]
International mathematics research notices, 2017 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
Jennifer S. Balakrishnan, Netan Dogra
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Reference Points and Effort Provision [PDF]
, 2011 A key open question for theories of reference-dependent preferences is what determines the reference point. One candidate is expectations: what people expect could affect how they feel about what actually occurs.
Abeler, Johannes +3 more
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Quadratic Chabauty and rational points, I: p-adic heights [PDF]
Duke mathematical journal, 2016 We give the first explicit examples beyond the Chabauty-Coleman method where Kim's nonabelian Chabauty program determines the set of rational points of a curve defined over $\mathbb{Q}$ or a quadratic number field. We accomplish this by studying the role
Jennifer S. Balakrishnan, Netan Dogra
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Thurston equivalence for rational maps with clusters [PDF]
, 2013 We investigate rational maps with period-one and period-two cluster cycles. Given the definition of a cluster, we show that, in the case where the degree is d and the cluster is fixed, the Thurston class of a rational map is fixed by the combinatorial ...
Thomas Sharland, Sharland, Thomas Joseph
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Covering Rational Surfaces with Rational Parametrization Images
Mathematics, 2021 Let S be a rational projective surface given by means of a projective rational parametrization whose base locus satisfies a mild assumption. In this paper we present an algorithm that provides three rational maps f,g,h:A2⇢S⊂Pn such that the union of the ...
Jorge Caravantes +3 more
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Rational points and zero-cycles on rationally connected varieties over number fields [PDF]
Algebraic Geometry, 2016 We report on progress in the qualitative study of rational points on rationally connected varieties over number fields, also examining integral points, zero-cycles, and non-rationally connected varieties.
Olivier Wittenberg
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Counting rational points on quadric surfaces
Discrete Analysis, 2018 Counting rational points on quadric surfaces, Discrete Analysis 2018:15, 29 pp. A _quadric hypersurface_ of dimension $D$ is the zero set of a quadratic form $Q$ in $D+2$ variables. If $Q(x_1,\dots,x_{D+2})=0$, then $Q(\lambda x_1,\dots,\lambda x_{D+2})=
Tim Browning, Roger Heath-Brown
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Birational Quadratic Planar Maps with Generalized Complex Rational Representations
Mathematics, 2023 Complex rational maps have been used to construct birational quadratic maps based on two special syzygies of degree one. Similar to complex rational curves, rational curves over generalized complex numbers have also been constructed by substituting the ...
Xuhui Wang +4 more
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All rational one-loop Einstein-Yang-Mills amplitudes at four points
Journal of High Energy Physics, 2018 All four-point mixed gluon-graviton amplitudes in pure Einstein-Yang-Mills theory with at most one state of negative helicity are computed at one-loop order and maximal powers of the gauge coupling, using D-dimensional generalized unitarity.
Dhritiman Nandan +2 more
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Many cubic surfaces contain rational points [PDF]
, 2017 Building on recent work of Bhargava, Elkies and Schnidman and of Kriz and Li, we produce infinitely many smooth cubic surfaces defined over the field of rational numbers that contain rational points.
T. Browning
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