نتایج جستجو برای: mordell
تعداد نتایج: 596 فیلتر نتایج به سال:
The Mordell-Lang conjecture and its variants assert subvarieties of algebraic groups can meet certain subgroups only in a finite set of translates of subgroups. In most cases the number of such translates is unknown and it is not even known whether this number may be bounded by a function of the geometric data. In this note we show that some uniformity follows immediately from the finiteness re...
We introduce a double zeta function of Mordell–Tornheim type and compute its values at nonpositive integer points. then discuss possible generalization the Kaneko–Zagier conjecture for all
We develop an algorithm computing the transcendental lattice and the Mordell–Weil group of an extremal elliptic surface. As an example, we compute the lattices of four exponentially large series of surfaces
Consider a smooth, geometrically irreducible, projective curve of genus $g\ge 2$ defined over number field degree $d \ge 1$. It has at most finitely many rational points by the Mordell Conjecture, theorem Faltings. We show that is bounded only in terms $g$, $d$ and Mordell–Weil rank curve's Jacobian, thereby answering affirmative question Mazur. In addition we obtain uniform bounds, $g$ $d$, fo...
We present the first examples of smooth elliptic Calabi-Yau threefolds with Mordell-Weil rank 10, highest currently known value. They are given by Schoen introduced Namikawa. explicitly compute Shioda homomorphism for generators group and their induced height pairing. There six isolated fibers Kodaira Type IV. Compactification F-theory on these gives an effective theory in dimensions which cont...
Faltings' theorem states that curves of genus g > 2 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the upper bound on the number of rational points [Szp85], XI, §2, but this bound is too large to be used in any reasonable sense. In 1985, Coleman showed [Col85] that Chabauty's method, which works when the Mordell-Weil ...
We make several observations about the category C of compact complex manifolds, considered as a many-sorted structure of finite Morley rank. We also point out that the Mordell-Lang conjecture holds for complex tori: if A is a complex torus, Γ a finitely generated subgroup of A, and X an analytic subvariety of A, then X ∩ Γ is a finite union of translates of subgroups of A. This is implicit in t...
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