18 citations · 29 across the 4 of their papers we have counts for
5 papers
A henselian preparation theorem
Laurent Moret-Bailly
We prove an analogue of the Weierstrass preparation theorem for henselian pairs, generalizing the local case recently proved by Bouthier and {\v C}esnavi{\v c}ius. As an applicatio…
Finite Morphisms to Projective Space and Capacity Theory
Ted Chinburg, Laurent Moret-Bailly, Georgios Pappas +1
We study conditions on a commutative ring R which are equivalent to the following requirement; whenever X is a projective scheme over S = Spec(R) of fiber dimension \leq d for some…
An extension of Greenberg's theorem to general valuation rings
Laurent Moret-Bailly
We extend Greenberg's strong approximation theorem to schemes of finite presentation over valuation rings with arbitrary value group, using the ultraproduct method of Becker, Denef…
Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic 0
Laurent Moret-Bailly, Alexandra Shlapentokh
Let be a one-variable function field over a field of constants of characteristic 0. Let be a holomorphy subring of , not equal to . We prove the following undecidabil…
Elliptic curves and Hilbert's tenth problem for algebraic function fields over real and p-adic fields
Laurent Moret-Bailly
Let k be a field of characteristic zero, V a smooth, positive-dimensional, quasiprojective variety over k, and D a nonempty effective divisor on V. Let K be the function field of V…