WEAK BLOCH-BEILINSON CONJECTURE FOR ZERO-CYCLES OVER p-ADIC FIELDS
نویسندگان
چکیده
Contents Introduction 2 1. Homology theory, cycle map, and Kato complex 6 2. Vanishing theorem 10 3. Bertini theorem over a discrete valuation ring 14 4. Surjectivity of cycle map 17 5. Blowup formula and moving lemma 19 6. Proof of main theorem 21 7. Applications of main theorem 23 References 25 1 2 SHUJI SAITO AND KANETOMO SATO
منابع مشابه
Cycles over Fields of Transcendence Degree One
We extend earlier examples provided by Schoen, Nori and Bloch to show that when a surface has the property that the kernel of its Albanese map is non-zero over the field of complex numbers, this kernel is non-zero over a field of transcendence degree one. This says that the conjecture of Bloch and Beilinson that this kernel is zero for varieties over number fields is precise in the sense that i...
متن کاملArithmetic Hodge Structure and Higher Abel-jacobi Maps
In this paper, we show some applications to algebraic cycles by using higher Abel-Jacobi maps which were defined in [the author: Motives and algebraic de Rham cohomology]. In particular, we prove that the Beilinson conjecture on algebraic cycles over number fields implies the Bloch conjecture on zero-cycles on surfaces. Moreover, we construct a zero-cycle on a product of curves whose Mumford in...
متن کاملTowards Connectivity for Codimension 2 Cycles: Infinitesimal Deformations
Let X be a smooth projective variety over an algebraically closed field k ⊂ C of characteristic zero, and Y ⊂ X a smooth complete intersection. The Weak Lefschetz theorem states that the natural restriction map H(X(C), Q) → H(Y (C), Q) on singular cohomology is an isomorphism for all i < dim(Y ). The Bloch-Beilinson conjectures on the existence of certain filtrations on Chow groups combined wit...
متن کاملFactorization of p-adic Rankin L-series
We prove that the p-adic L-series of the tensor square of a p-ordinary modular form factors as the product of the symmetric square p-adic L-series of the form and a Kubota– Leopoldt p-adic L-series. This establishes a generalization of a conjecture of Citro. Greenberg’s exceptional zero conjecture for the adjoint follows as a corollary of our theorem. Our method of proof follows that of Gross, ...
متن کاملOn the p-adic Beilinson conjecture for number fields
We formulate a conjectural p-adic analogue of Borel’s theorem relating regulators for higher K-groups of number fields to special values of the corresponding ζ-functions, using syntomic regulators and p-adic L-functions. We also formulate a corresponding conjecture for Artin motives, and state a conjecture about the precise relation between the p-adic and classical situations. Parts of the conj...
متن کامل