WebTheorem 5. Let Sbe a nite set of places of number eld K:Then there are only nitely many isogeny classes of abelian varieties of a given dimension gwith good reduction outside S: … http://math.stanford.edu/~vakil/0708-216/216class01.pdf
Faltings’ Finiteness Theorems on Abelian Varieties and Curves
WebJul 26, 2024 · Falting's proof of Mordell's conjecture is one of the greatest achievements in arithmetic geometry. Broadly speaking, it capitalizes on an earlier observation of Parshin, which reduces Mordell's conjecture to a conjecture of Shafarevich. ... For which fields does the isogeny theorem hold. 4. question regarding Faltings' proof of the Tate ... Web1) A theory of differentiation with respect to the ground field. A well-known consequence of such a theory could include an array of effective theorems in Diophantine geometry, like an effective Mordell conjecture or the ABC conjecture. Over function fields, the ability to differentiate with respect to the field of constants is responsible for ... rakim discogs
Talk:Faltings
WebNov 2, 2015 · 1. Big portion of arithmetic geometry revolves around elliptic curves and abelian varieties. As you already have good background in Number Theory both algebraic and analytic, once you've become familiar with the basic algebraic geometry (say, from Hartshorne's book and/or Ravi Vakil's Foundations and/or Qing Liu's Algebraic Geometry … WebTheorem 2.1 (Tate’s conjecture). Let A and B be two abelian varieties over K and let ‘ be a prime. Then the natural map Hom(A, B) Z ‘! Hom Z[G K](T ‘A, T ‘B) is an isomorphism. Theorem 2.2 (Semisimplicity Theorem). Let A be an abelian variety over K and let ‘ be a prime. Then the action of G K on V ‘A is semisimple. 1 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 … rakimeco