Tangent star cones.
The differential spectrum of a ring
The divisor of the resultant.
The equations of the abelian surfaces embedded in ...4 (...).
The field of definition of the Mordell-Weil group of an elliptic curve over a function field
The singular sets of a complex of modules.
The spectrum associated to a radical operation.
Théorèmes de préparation Gevrey et étude de certaines applications formelles
We consider subrings A of the ring of formal power series. They are defined by growth conditions on coefficients such as, for instance, Gevrey conditions. We prove preparation theorems of Malgrange type in these rings. As a consequence we study maps F from to without constant term such that the rank of the Jacobian matrix of F is equal to 1. Let be a formal power series. If F is a holomorphic map, the following result is well known: ∘ F is analytic implies there exists a convergent power series...
Towards a General Theory of Formally ...-Adic Fields.