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Seminar on Faltings's Theorem. Spring 2016. Mondays 9:30am-11:00am at SC 232. Feb 19:30-11am SC 232Harvard Chi-Yun Hsu Tate's conjecture over finite By Faltings' theorem, and known simple results, a curve is arithmetically dense if and only if its genus is < 1. As for varieties of arbitrary dimension, see an account The topic for 2010-2011 is Faltings' proof of the Mordell conjecture.
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In number theory, the Mordell conjecture stated a basic result regarding the rational number solutions to Diophantine equations. It was eventually proved by Gerd Faltings in 1983, about six decades after the conjecture was made; it is now known as Faltings' theorem. Faltings's theorem — Wikipedia Republished // WIKI 2 Great Wikipedia has got greater. From Wikipedia, the free encyclopedia In number theory, the Mordell conjecture is the conjecture made by Mordell (1922) that a curve of genus greater than 1 over the field Q of rational numbers has … Faltings's original proof used the known reduction to a case of the Tate conjecture, and a number of tools from algebraic geometry, including the theory of Néron models.
Faltings produktsats – Wikipedia
Save The main goal of this seminar will be understanding the new proof of the Mordell conjecture (Theorem of Faltings [F]) given by Lawrence and Venkatesh [LV]. 18 Sep 2015 Abstract: In this talk we'll discuss Diophantine equations, elliptic curves, and a nice application of Falting's Theorem. No prerequisites are mat's Last Theorem, it turns out that we can use tools from That Fermat's Last Theorem is easy to prove for Faltings' Theorem née Mordell's Conjecture. As is well known,.
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Introduction. Let K be a finite extension of 10, A an abelian variety defined A CONTRIBUTION TO THE THEORY OF FORMAL.
It was introduced by Faltings ( 1991 ) in his proof of Lang's conjecture that subvarieties of an abelian variety containing no translates of non-trivial abelian subvarieties have only finitely many rational points. Faltings's theorem. In number theory, the Mordell conjecture is the conjecture made by Mordell (1922) that a curve of genus greater than 1 over the field Q of rational numbers has only finitely many rational points. The conjecture was later generalized by replacing Q by any number field. It was proved by Gerd Faltings (1983), and is now known as
The Isogeny theorem that abelian varieties with isomorphic Tate modules (as Q ℓ-modules with Galois action) are isogenous. A sample application of Faltings's theorem is to a weak form of Fermat's Last Theorem : for any fixed n > 4 there are at most finitely many primitive integer solutions (pairwise coprime solutions) to a n + b n = c n , since for such n
Because of the Mordell-Weil theorem, Faltings' theorem can be reformulated as a statement about the intersection of a curve C with a finitely generated subgroup Γ of an abelian variety A. Generalizing by replacing C by an arbitrary subvariety of A and Γ by an arbitrary finite-rank subgroup of A leads to the Mordell-Lang conjecture, which has been proved. Inom matematiken är Faltings produktsats ett resultat som ger tillräckliga villkor för en delvarietet av en produkt av projektiva rum för att vara en produkt av varieteter i projektiva rummen.
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In 1983 it was proved by Gerd Faltings (1983, 1984), and is now known as Faltings's theorem.
FINITENESS THEOREMS FOR ABELIAN VARIETIES.
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Finiteness of abelian varieties and Modular Heights.
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Theorem: Let k be an Proof of Faltings' theorem of the finiteness of the l-adic Galois representations with fixed Serre weights and bounded ramification. References: [\SS 2.5&2.7; Dar], [Del] Speaker: Shilung W. Schedule: 30/04, at 14:00.
Faltings was the formal supervisor of Shinichi Mochizuki, Wieslawa Niziol, Nikolai Dourov. Awards and honours. Fields Medal (1986) Guggenheim Fellowship (1988/89) Gottfried Wilhelm Leibniz Prize (1996) King Faisal International Prize (2014) Shaw Prize (2015) Foreign Member of the Royal Society (2016) Cantor Medal (2017) For a finitely generated field over a number field the theorem holds by work of Faltings, if I am not mistaken. See the book by Faltings-Wüstholz on the Mordell conjecture (I don't have it at hand). $\endgroup$ – Damian Rössler Dec 20 '12 at 21:15