This book provides an introduction to a topic of central interest in transcendental algebraic
geometry: the Hodge conjecture. Consisting of 15 lectures plus addenda and appendices …

We prove that the adic algebraic monodromy groups associated to a motive over a number
field are generated by certain one parameter subgroups determined by Hodge numbers. In …

arXiv:alg-geom/9709030v1 26 Sep 1997 Page 1 arXiv:alg-geom/9709030v1 26 Sep 1997 ).
matters. Appendix B. A Survey of the Hodge Conjecture for Abelian Varieties by B. Brent …

Families of Motives and the Mumford–Tate Conjecture Page 1 Families of Motives and the
Mumford–Tate Conjecture Ben Moonen Abstract. We give an overview of some results and …

Let A be an abelian variety over a number field K. It was conjectured by S. Lang that the
image of Galois in the adelic-Galois representation associated to the Tate modules of A …

In this note, we prove an adelic open image theorem for abelian schemes and, more
generally, families of-motives. This result, which can be interpreted as an adelic …

Soit A une variété abélienne définie sur un corps de nombres K. Le nombre de points de
torsion définis sur une extension finie L est borné polynomialement en terme du degré [L: K] …

Suppose that H is a semisimple-subgroup of G such that YH (IR)/Kn is also Hermitian
symmetric, with Kn Koo c H a maximal, compact subgroup of H (IR), and such that the …

Suppose X is an abelian variety defined over a field F,~ is a prime number, and, f~ char (F).
Let F'denote a separable closure of F, let T~(X)= lim XI,-(the Tate module), let V~(X)= Ti (X) …

We make explicit Serre's generalization of the Sato-Tate conjecture for motives, by
expressing the construction in terms of fiber functors from the motivic category of absolute …