Relevant bibliographies by topics / Number theory – Arithmetic algebraic geometry (Diophantine geometry) – Heights

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Academic literature on the topic 'Number theory – Arithmetic algebraic geometry (Diophantine geometry) – Heights'

Author: Grafiati
Published: 4 June 2021
Last updated: 2 February 2022

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Dissertations / Theses on the topic "Number theory – Arithmetic algebraic geometry (Diophantine geometry) – Heights"

1

Tyler, Michael Peter. "On the birational section conjecture over function fields." Thesis, University of Exeter, 2017. http://hdl.handle.net/10871/31600.

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The birational variant of Grothendieck's section conjecture proposes a characterisation of the rational points of a curve over a finitely generated field over Q in terms of the sections of the absolute Galois group of its function field. While the p-adic version of the birational section conjecture has been proven by Jochen Koenigsmann, and improved upon by Florian Pop, the conjecture in its original form remains very much open. One hopes to deduce the birational section conjecture over number fields from the p-adic version by invoking a local-global principle, but if this is achieved the problem remains to deduce from this that the conjecture holds over all finitely generated fields over Q. This is the problem that we address in this thesis, using an approach which is inspired by a similar result by Mohamed Saïdi concerning the section conjecture for étale fundamental groups. We prove a conditional result which says that, under the condition of finiteness of certain Shafarevich-Tate groups, the birational section conjecture holds over finitely generated fields over Q if it holds over number fields.
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Faye, Bernadette. "Diophantine equations with arithmetic functions and binary recurrences sequences." Thesis, 2017. https://hdl.handle.net/10539/24996.

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A thesis submitted to the Faculty of Science, University of the Witwatersrand and to the University Cheikh Anta Diop of Dakar(UCAD) in fulfillment of the requirements for a Dual-degree for Doctor in Philosophy in Mathematics. November 6th, 2017.
This thesis is about the study of Diophantine equations involving binary recurrent sequences with arithmetic functions. Various Diophantine problems are investigated and new results are found out of this study. Firstly, we study several questions concerning the intersection between two classes of non-degenerate binary recurrence sequences and provide, whenever possible, effective bounds on the largest member of this intersection. Our main study concerns Diophantine equations of the form '(jaunj) = jbvmj; where ' is the Euler totient function, fungn 0 and fvmgm 0 are two non-degenerate binary recurrence sequences and a; b some positive integers. More precisely, we study problems involving members of the recurrent sequences being rep-digits, Lehmer numbers, whose Euler’s function remain in the same sequence. We prove that there is no Lehmer number neither in the Lucas sequence fLngn 0 nor in the Pell sequence fPngn 0. The main tools used in this thesis are lower bounds for linear forms in logarithms of algebraic numbers, the so-called Baker-Davenport reduction method, continued fractions, elementary estimates from the theory of prime numbers and sieve methods.
LG2018
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Books on the topic "Number theory – Arithmetic algebraic geometry (Diophantine geometry) – Heights"

1

Arakelov geometry. Providence, Rhode Island: American Mathematical Society, 2014.

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International Workshop on Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms (2011 Banff, Alta.). Diophantine methods, lattices, and arithmetic theory of quadratic forms: International workshop, Banff International Research Station, November 13-18, 2011, Banff, Alberta, Canada. Edited by Chan, Wai Kiu, 1967- editor of compilation, Fukshansky, Lenny, 1973- editor of compilation, Schulze-Pillot, Rainer, editor of compilation, and Vaaler, Jeffrey D., editor of compilation. Providence, Rhode Island: American Mathematical Society, 2013.

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Tschinkel, Yuri, Carlo Gasbarri, Steven Lu, and Mike Roth. Rational points, rational curves, and entire holomorphic curves on projective varieties: CRM short thematic program, June 3-28, 2013, Centre de Recherches Mathematiques, Universite de Montreal, Quebec, Canada. Providence, Rhode Island: American Mathematical Society, 2015.

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Capacity theory with local rationality: The strong Fekete-Szegő theorem on curves. Providence, Rhode Island: American Mathematical Society, 2013.

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The geometric and arithmetic volume of Shimura varieties of orthogonal type. Providence, Rhode Island, USA: American Mathematical Society, 2014.

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Brauer groups, Tamagawa measures, and rational points on algebraic varieties. Providence, Rhode Island: American Mathematical Society, 2014.

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1953-, Campillo Antonio, ed. Zeta functions in algebra and geometry: Second International Workshop on Zeta Functions in Algebra and Geometry, May 3-7, 2010, Universitat de Les Illes Balears, Palma de Mallorca, Spain. Providence, R.I: American Mathematical Society, 2012.

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Colliot-Thélène, J. L. Arithmetic algebraic geometry. Edited by Kato K, Vojta Paul 1957-, Ballico E. 1955-, and Centro internazionale matematico estivo. Berlin: Springer-Verlag, 1993.

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International Conference Arithmetic, Geometry, Cryptography and Coding Theory (14th 2013 Marseille, France). Algorithmic arithmetic, geometry, and coding theory: 14th International Conference, Arithmetic, Geometry, Cryptography, and Coding Theory, June 3-7 2013, CIRM, Marseille, France. Edited by Ballet Stéphane 1971 editor, Perret, M. (Marc), 1963- editor, and Zaytsev, Alexey (Alexey I.), 1976- editor. Providence, Rhode Island: American Mathematical Society, 2015.

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Quantitative arithmetic of projective varieties. Basel: Birkhäuser, 2009.

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