Part (I): The semi-reduction theorem.

Let A be an abelian variety defined over K, the field of fraction of a henselian ring R. In this talk, we shall explain the construction of the Tate module T_l (A) and the different objects naturally associated to the Neron model of A (in the case, when the parameter l is different from p, the residual characteristic of R). We shall see that the main properties of the Neron model of A can be interpreted in terms of the action of the group of monodromy on the Tate module. Also we will try to outline the proof of the semi-reduction theorem of Grothendieck.

 

References:

Grothendieck: Expose IX (Modeles de Neron et Monodromie) Groupes de monodromie en geometrie algerique. I. Séminaire de Géométrie Algébrique du Bois-Marie 1967–1969 (SGA 7 I).