Faltings isogeny theorem

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August undefined, 2024

WebNov 1, 2024 · By Faltings' isogeny theorem [3], we have rk Z (End (A)) = dim Q ℓ ⁡ (End (A) ⊗ Q ℓ) = dim Q ℓ ⁡ (End G ℓ (V ℓ (A))). Observing that homotheties centralize V ℓ ( A ) ⊗ V ℓ ( A ) ∨ and that Weyl's unitarian trick allows us to pass from G ℓ 1 to the maximal compact subgroup ST ( A ) , we obtain dim Q ℓ ⁡ ( V ℓ ( A ... WebJun 3, 2011 · The following theorem connects the inseparable degree of an isogeny with the height of the associated map of formal groups in positive characteristic. Combining it …

The Tate Conjecture from Finiteness - Zuse Institute Berlin

WebOur plan is to try to understand Faltings’s proof of the Mordell conjecture. The focus will be on his first proof, which is more algebraic in nature, proves the Shafarevich and Tate conjectures, and also gives us a chance to learn about some nearby topics, such as the moduli space of abelian varieties or p-adic Hodge theory. WebMar 6, 2024 · The Mordell conjecture that a curve of genus greater than 1 over a number field has only finitely many rational points; The Isogeny theorem that abelian varieties … scams on craigslist cars

Faltings

WebA·. Also in another paper we will apply our isogeny estimates directly to obtain quantitative versions of 5erre's we11-known theorem [Se] on Galois groups of division fields of elliptic curves. Dur proof of Finiteness I is rather different from Faltings's proof, and it is interesting to compare the two approaches. Web2. Effective version of Faltings’ theorem One important input of our main theorem is an e ective version of Faltings’ isogeny theorem. Such a theorem was rst proved by … WebThe proof uses a crystalline analogue of Faltings’ isogeny theorem due to Bost and the known cases of the Mumford–Tate conjecture. AB - In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. This notion is a crystalline analogue of -adic Tate cycles. sayre train station

Formal groups and the isogeny theorem - Project Euclid

Faltings’ Finiteness Theorems on Abelian Varieties and Curves

WebThese theorems were outstanding conjectures regarded as having independent interest. Faltings proved them all simultaneously with the Mordell conjecture. In retrospect, it is … WebApr 20, 2013 · Remark 10 For finite fields was proved by Tate himself soon after its formulation, now known as Tate's isogeny theorem. Zarhin [7] proved the case of … scams on craigslist buying carsWebThen a Weil restriction argument, together with Faltings’ isogeny theorem, allows one to conclude. We now explain the new ingredients in turn, highlighting the additional diﬃculties. Remark 1.7 (Sketch of the proof of Theorem 1.4). Again for notational simplicity, assume that Lcorresponds to a representation: ρ: π1(UK) →GL2(Zℓ),. scams on discogs

"WebJan 21, 2024 · Harry Smit Faltings's isogeny theorem states that two abelian varieties are isogenous over a number field precisely when the characteristic polynomials of the reductions at almost all prime ideals of the number field agree. " - Faltings isogeny theorem

Faltings isogeny theorem

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WebApr 11, 2015 · Theorem 1: Let X ⊂ A be a subvariety. If X contains no translates of abelian subvarieties of A, then X ( K) is finite. Theorem 2: Let U be an affine open subset of A … WebDec 19, 2008 · The rationality is applied to give a direct construction of isogenies between new quotients of Jacobians of Shimura curves, completely independent of Faltings’ isogeny theorem. Download to read the full article text References Baruch, E.M., Mao, Z.: Central values of automorphic L -functions. Geom. Funct. Anal. 17 (2), 333–384 (2007)

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WebThese classes include abelian varieties of prime dimension that have nontrivial endomorphism ring. The proof uses a crystalline analogue of Faltings’ isogeny theorem due to Bost and the known cases of the Mumford–Tate conjecture. We also discuss some strengthenings of the theorem of Bost. Terms of Use WebIn arithmetic geometry, Faltings' product theorem gives sufficient conditions for a subvariety of a product of projective spaces to be a product of varieties in the projective …

WebThe key statement is the so-called Faltings’s niteness theorem, which says that each isogeny class over the number eld K only contains nitely many isomorphism classes. … Webquences of Faltings isogeny theorem; this implies, for example, that if Aand A′ satisfy (1.1), then Aand A′ share the same endomorphism ﬁeld K. We then show that the result by Rajan mentioned above implies that the local-global QT prin-ciple holds for those abelian varieties Asuch that End(AQ) = Z. We conclude §2

WebBy Serre's isogeny theorem, E is modular (in the sense of being a factor of the Jacobian of a modular curve). This is the step which confuses me. The question I am asking is: can anyone explain in more detail why Serre's (/Faltings's) isogeny theorem tells us that since ρ E, 3 is modular, there is a non-constant morphism X 0 ( N) → E? WebAbstract. In this chapter we shall state the finiteness theorems of Faltings and give very detailed proofs of these results. In the second section we shall beginn with the …

Faltings's 1983 paper had as consequences a number of statements which had previously been conjectured: • The Mordell conjecture that a curve of genus greater than 1 over a number field has only finitely many rational points; • The Isogeny theorem that abelian varieties with isomorphic Tate modules (as -modules with Galois action) are isogenous.

http://virtualmath1.stanford.edu/~conrad/mordellsem/Notes/L03.pdf sayre to syracuseWebOne of the spectacular consequences of the analytic subgroup theorem was the Isogeny Theorem published by Masser and Wüstholz. A direct consequence is the Tate conjecture for abelian varieties which Gerd Faltings had proved with totally different methods which has many applications in modern arithmetic geometry. scams on craigslist rentalshttp://math.stanford.edu/~conrad/mordellsem/Notes/L20.pdf scams on craigslist jobsWebFlattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution respectively.Other terms used are ellipticity, or … sayre tractor supplyWebJan 15, 2001 · His theorem unifies and generalizes results of Chudnovsky's and Y. Andr\'e, motivated by an arithmetic conjecture of Grothendieck that predicts that the solutions of certain differential equations ... scams on craigslist vacation rentalsWebMar 8, 2012 · One of the key steps in proving Faltings' theorem is to prove the finiteness theorems of abelian varieties. Theorem 2 (Finiteness I, or Conjecture T) Let be an abelian variety over a number field . Then there are only finitely many isomorphism classes of abelian varieties over isogenous to . sayre turkey trot resultsWebJan 21, 2024 · Faltings's isogeny theorem states that two abelian varieties are isogenous over a number field precisely when the characteristic polynomials of the reductions at almost all prime ideals of the ... sayre turkey trot 2022