Relations in the Cremona group over a perfect field

Elliptic Curves over the Perfect Closure of a Function Field

We prove that the group of rational points of a non-isotrivial elliptic curve defined over the perfect closure of a function field in positive characteristic is finitely generated.

Appendix A . The Cremona group is not an amalgam Yves

Let k be a field. The Cremona group Bir(Pk) of k in dimension d is defined as the group of birational transformations of the d-dimensional k-affine space. It can also be described as the group of k-automorphisms of the field of rational functions k(t1, . . . , td). We endow it with the discrete topology. Let us say that a group has Property (FR)∞ if it satisfies the following (1) For every isom...

On Perfect Subfields over Which a Field Is Separably Generated

In this paper, we determine the perfect subfields over which a field is separably generated. Let a field F of characteristic. p^O be an extension of a field £. A separating transcendence basis for the extension £/£ is a transcendence basis B of £/£ such that £ is a separable algebraic extension of £(£). If £/£ has a separating transcendence basis, we say that £ is separably generated over £. A ...

Ramification theory for varieties over a perfect field

If p2 : Γ → U is proper, Γ∗ = pr1∗ ◦ pr∗ 2 : H c (U,Q ) → H c (U,Q ) is defined. Write Tr(Γ∗ : H∗ c (UF̄ ,Q )) = ∑2d q=0(−1)Tr(Γ : H c (UF̄ ,Q )). Assume X: smooth U ⊂ X: the complement of a divisor D = D1 ∪ · · · ∪ Dm with simple normal crossings. Define p : (X ×X)′ → X ×X: the blow-up at D1 ×D1, . . . , Dm ×Dm ∆X = X → (X ×X)′: the log diagonal. Theorem 1.2 Let Γ̄′ be the closure of Γ in (X ×X)′...

Finite abelian subgroups of the Cremona group of the plane