منابع مشابه
The Weil Conjecture for K3 Surfaces
Denote by Fq a field of q elements, F̄q an algebraic closure of Fq, φ ∈ Gal(F̄q/Fq) the Frobenius substitution x 7→ xq and F = φ−1 the “geometric Frobenius”. Denote by X a scheme (separated of finite type) over Fq, and denote by X̄ the scheme over F̄q obtained by extension of scalars. For all closed points x of X, let deg(x) = [k(x) : Fq] be the degree over Fq of the residue extension. The zeta fun...
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Vojta’s Conjectures are well known to imply a wide range of results, known and unknown, in arithmetic geometry. In this paper, we add to the list by proving that they imply that rational points tend to repel each other on algebraic varieties with nonnegative Kodaira dimension. We use this to deduce, from Vojta’s Conjectures, conjectures of Batyrev-Manin and Manin on the distribution of rational...
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We use a result of van Geemen [vG4] to determine the endomorphism algebra of the Kuga–Satake variety of a K3 surface with real multiplication. This is applied to prove the Hodge conjecture for self-products of double covers of P which are ramified along six lines.
متن کاملFiniteness of K3 Surfaces and the Tate Conjecture
Given a finite field k of characteristic p ≥ 5, we show that the Tate conjecture holds for K3 surfaces over k if and only if there are finitely many K3 surfaces defined over each finite extension of k.
متن کاملOn the cyclic Formality conjecture
We conjecture an explicit formula for a cyclic analog of the Formality L∞-morphism [K]. We prove that its first Taylor component, the cyclic Hochschild-Kostant-Rosenberg map, is in fact a morphism (and a quasiisomorphism) of the complexes. To prove it we construct a cohomological version of the Connes-Tsygan bicomplex in cyclic homology. As an application of the cyclic Formality conjecture, we ...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2019
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x19007206