北大数論セミナー：Semi-stable reduction and finite monodromy groups of abelian varieties

Time： 10:30 – 11:30

Place：理学部3号館3-307室　　　

Speaker：S\’everin Philip 氏（RIMS）

Title： Semi-stable reduction and finite monodromy groups of abelian varieties

Abstract：We will introduce the question of the degree of semi-stable reduction of abelian varieties starting with the case of elliptic curves and recalling the semi-stable reduction theorem of Grothendieck. We will present an effective form (for the degree of the extension), depending only on the dimension of the variety, of this theorem. The main objects for this result are the finite monodromy groups of abelian varieties which we will introduce with their basic properties. We will then see how these groups provide a computation for the semi-stability degree of an abelian variety (i.e. the smallest degree of a field extension over which it has semi-stable reduction) and how they satisfy a form of local-global principle. In the last part, we will show a characterisation of the finite monodromy groups of abelian varieties over number fields in fixed dimension by automorphism of semi-abelian varieties over finite fields. The construction is made using integral p-adic Hodge theory, degeneration and descent arguments.

Organizer：安田 正大