This paper is about the structure of families of open ideals in the ring [italic]R of power series in two variables. The Hilbert scheme Hilb[italic superscript]n [italic]R parametrizing them is stratified into locally closed subschemes [italic]Z[italic subscript]T, whose dimensi…
Pseudofunctors with values on modules with zero dimensional support are constructed over the formally smooth category and residually finite category. Combining those pseudofunctors, a pseudofunctor over the category whose objects are Noetherian local rings and whose morphisms a…
The Berkovich Line over Z This text is devoted to the study of the Berkovich line over the ring of integers of a number field. It is a geometric object which naturally contains complex analytic lines (or their quotient by conjugation), associated to the infinite places, and clas…