EuDML | Browse

In this paper we consider questions of the following type. Let $k$ be a base field and $K / k$ be a field extension. Given a geometric object $X$ over a field $K$ (e.g. a smooth curve of genus $g$ ), what is the least transcendence degree of a field of definition of $X$ over the base field $k$ ? In other words, how many independent parameters are needed to define $X$ ? 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

Dorette A. Pronk (1996)

Compositio Mathematica

Étude de certains éclatements

Marguerite Flexor (1972)

Bulletin de la Société Mathématique de France

Every Algebraic Set in n-Space Is the Intersection of n Hypersurfaces.

David Eisenbud, E. Graham Jr. Evans (1973)

Inventiones mathematicae

Explicit cogenerators for the homotopy category of projective modules over a ring

Amnon Neeman (2011)

Annales scientifiques de l'École Normale Supérieure

Let $R$ be a ring. In two previous articles [12, 14] we studied the homotopy category $𝐊 (R - Proj)$ of projective $R$ -modules. We produced a set of generators for this category, proved that the category is $ℵ_{1}$ -compactly generated for any ring $R$ , and showed that it need not always be compactly generated, but is for sufficiently nice $R$ . We furthermore analyzed the inclusion $j_{!}^{} : 𝐊 (R - Proj) \to 𝐊 (R - Flat)$ and the orthogonal subcategory $𝒮 = {𝐊 (R - Proj)}^{⊥}$ . And we even showed that the inclusion $𝒮 \to 𝐊 (R - Flat)$ has a right adjoint; this forces some natural map to be an equivalence...

Exposé on a conjecture of Tougeron

Joseph Becker (1977)

Annales de l'institut Fourier

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 $η$ is an analytic curve on an analytic variety $V$ and $f$ is a formal power series which is convergent when restricted...

Extension of the concept of n-function to categories

Lintz, R.G. (1987)

Portugaliae mathematica

Displaying 21 – 33 of 33

Currently displaying 21 – 33 of 33