Length 2 variables of A[x,y] and transfer

Abstract

Length 2 variables of A[x, y] and transfer by Eric Edo (Talence) and Stéphane Vénéreau (Grenoble)

The strong Nagata conjecture

“…As an immediate consequence, all coordinates of P 2 are tame as well. Nagata (8) conjectured in 1972 that there exist wild automorphisms in Aut K P 3 . The famous Nagata conjecture was recently proved by Shestakov and Umirbaev (9)(10)(11).…”

Coordinates in two variables over a $\mathbb {Q}$-algebra

“…The latter paper clearly demonstrates the importance of studying coordinates in two variables over commutative rings by showing how it leads to many interesting coordinates in dimensions greater than two. Even more recently, extending the results of [EV01], a large class of coordinates in two variables over commutative rings was studied by Berson in [Ber02]. This paper gives several criteria (Theorems 3.2, 3.4, and 3.5) to decide if a given polynomial in two variables over a commutative Q-algebra is a coordinate.…”

Coordinates ofR[x,y]: Constructions and Classifications

“…[11] with the case p 2 = 1 and in [9] for the case p 1 R + p 2 R = R. The case p 2 = 1 also appear independently in [8] (see also [17] §9.4) in the case…”