Discrete tomography and the Hodge conjecture for certain abelian varieties of CM-type
نویسندگان
چکیده
منابع مشابه
Some Remarks on the Hodge Conjecture for Abelian Varieties
Let X be a smooth complex projective variety of dimension g. A Hodge class of degree 2d on X is, by definition, an element of H(X,Q)∩H(X). The cohomology class of an algebraic subvariety of codimension d of X is a Hodge class of degree 2d. The classical Hodge conjecture states that any Hodge class on X is algebraic, i.e., a Q-linear combination of classes of algebraic subvarieties of X. Lefsche...
متن کاملAn Inductive Approach to the Hodge Conjecture for Abelian Varieties
Let X be a smooth complex projective variety of dimension g. A Hodge class of degree 2d on X is, by definition, an element of H(X,Q)∩H(X). The cohomology class of an algebraic subvariety of codimension d of X is a Hodge class of degree 2d. The original Hodge conjecture states that any Hodge class on X is algebraic, i.e., a Q-linear combination of classes of algebraic subvarieties of X. Lefschet...
متن کاملThe 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 ...
متن کاملThe Hodge Conjecture for General Prym Varieties
We work over C, the field of complex numbers. The Prym variety of a double cover C → D of a smooth connected projective curve D by a smooth connected curve C is defined (see [7]) as the identity component of the kernel of the norm homomorphism N : J(C) → J(D) between the Jacobians of the curves. This is an abelian variety polarised by the restriction of the canonical polarisation on J(C); we de...
متن کاملHodge cycles on abelian varieties
This is a TeXed copy of – Hodge cycles on abelian varieties (the notes of most of the seminar “Périodes des Intégrales Abéliennes” given by P. Deligne at I.H.E.S., 1978–79; pp9– 100 of Deligne et al. 1982). somewhat revised and updated. See the endnotes1 for more details.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 2006
ISSN: 0386-2194
DOI: 10.3792/pjaa.82.25