The tame fundamental group of an abelian variety and integral points

For example, the following result was proved: a cyclic group of prime order is conjugate to a linear automorphism of the plane if and only if it does not fix a curve of positive

In the last section we deduce a generalization to arbitrary character- istic of Serre's formula for the pairing on the first de Rham cohomology group of a curve over a field

We use multiplicative notation for abelian group operation, except in Section 3. Most of our notation is standard and refers to [4] and [6]. Power automorphisms of an

LEMMA 4.3.. Suppose that G is an infinite nonabelian C14*- group.. Therefore there is an infinite set C of conjugates of u whose squares are distinct. By Theorem 4.1,

is a canonical decomposition of the collineation group 0152 == G fG with respect to its reduced symplectic structure (cf. III below). They play a very useful role

upper bound for the conductor of elliptic curves in general and ask for the behavior of the conductor of an abelian variety in the case of wild ramification.. We

When (c) holds, there is a one-to-one onto correspondence between primitive idempotents in KG and isomorphism classes of irreducible KG-modules with finite centralizer

o- and T are surjective, and Pic(XJ -> Pic(X^) maps the kernel of a isomorphically onto the kernel of T (cf. E) is the fpqc sheaf associated to the functor H°(^) (resp. .)