On the integral Tate conjecture for finite fields and representation theory
نویسندگان
چکیده
منابع مشابه
The Tate Conjecture for Certain Abelian Varieties over Finite Fields
In an earlier work, we showed that if the Hodge conjecture holds for all complex abelian varieties of CM-type, then the Tate conjecture holds for all abelian varieties over finite fields (Milne 1999b). In this article, we extract from the proof a statement (Theorem 1.1) that sometimes allows one to deduce the Tate conjecture for the powers of a single abelian variety A over a finite field from ...
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These are my notes for a talk at the The Tate Conjecture workshop at the American Institute of Mathematics in Palo Alto, CA, July 23–July 27, 2007, somewhat revised and expanded. The intent of the talk was to review what is known and to suggest directions for research. v1 (September 19, 2007): first version on the web. v2 (October 10, 2007): revised and expanded. v2.1 (November 7, 2007) Minor f...
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In this lecture, we discuss the proof of the Tate conjecture for abelian varieties over number fields as presented in Falting’s seminal paper "Finiteness Theorems for Abelian Varieties over Number Fields" [3]. We will follow his argument closely adding additional details as needed. This is the beginning of the payoff of all our work throughout this seminar so I will freely reference and quote r...
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Recently N. Levin proved the Tate conjecture for ordinary cubic fourfolds over finite fields. In this paper we prove the Tate conjecture for selfproducts of ordinary cubic fourfolds. Our proof is based on properties of so called polynomials of K3 type introduced by the author about a dozen years ago.
متن کاملThe Tate conjecture for cubic fourfolds over a finite field
If X/F is a smooth projective variety over a finite field F of characteristic p > 0 and X = X ⊗ F, there is a cycle class map CH(X)→ H et (X,Q`(i)) for ` 6= p from the Chow group of codimension i cycles on X to étale cohomology. The image of this map lies in the subspace of H et (X,Q`(i)) which is invariant under the natural Galois action. In [T3], Tate conjectures that, in fact, this subspace ...
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ژورنال
عنوان ژورنال: Algebraic Geometry
سال: 2016
ISSN: 2214-2584
DOI: 10.14231/ag-2016-007