Erratum : «Sur la compacité du spectre minimal d'un anneau»
Espaces analytiques sous-algébriques
Espaces de Moisezon relatifs et algébrisation des modifications analytiques.
Essential dimension of moduli of curves and other algebraic stacks
In this paper we consider questions of the following type. Let be a base field and be a field extension. Given a geometric object over a field (e.g. a smooth curve of genus ), what is the least transcendence degree of a field of definition of over the base field ? In other words, how many independent parameters are needed to define ? To study these questions we introduce a notion of essential dimension for an algebraic stack. Using the resulting theory, we give a complete answer to...
Etendues and stacks as bicategories of fractions
Étude de certains éclatements
Every Algebraic Set in n-Space Is the Intersection of n Hypersurfaces.
Explicit cogenerators for the homotopy category of projective modules over a ring
Let be a ring. In two previous articles [12, 14] we studied the homotopy category of projective -modules. We produced a set of generators for this category, proved that the category is -compactly generated for any ring , and showed that it need not always be compactly generated, but is for sufficiently nice . We furthermore analyzed the inclusion and the orthogonal subcategory . And we even showed that the inclusion has a right adjoint; this forces some natural map to be an equivalence...
Exposé on a conjecture of Tougeron
An algebra homomorphism of the locatized affine rings of an algebraic variety is continuous in the Krull topology of the respective local rings. It is not necessarily open or closed in the Krull topology. However, we show that the induced map on the associated analytic local rings is also open and closed in the Krull topology. To do this we prove a conjecture of Tougeron which states that if is an analytic curve on an analytic variety and is a formal power series which is convergent when restricted...
Extension of the concept of n-function to categories
Finiteness results for Abelian tree models
Equivariant tree models are statistical models used in the reconstruction of phylogenetic trees from genetic data. Here equivariant§ refers to a symmetry group imposed on the root distribution and on the transition matrices in the model. We prove that if that symmetry group is Abelian, then the Zariski closures of these models are defined by polynomial equations of bounded degree, independent of the tree. Moreover, we show that there exists a polynomial-time membership test for that Zariski closure....
First-order definability and algebraicity of the sets of annihilating and generating collections of elements for some relatively free solvable groups.
Flat modules in algebraic geometry
For a Nonclosing Field, Every Algebraic Variety is a Hypersurface, or All of Space.
For a Nonclosing Field, Every Algebraic Variety is a Hypersurface, or All of Space. (Short Communication).
Formal functions on homogeneous spaces.
Fortsetzung von Spezialisierungen: ein idealtheoretischer Zugang
Foundations of the theory of Fano schemes
-тождества и -многообразия
-тождества нильпотентных групп. I