We show that a homomorphism of algebras is a categorical epimorphism if and only if all induced morphisms of the associated module varieties are immersions. This enables us to classify all minimal singularities in the subvarieties of modules from homogeneous standard tubes.
We prove that every injective endomorphism of an affine algebraic variety over an algebraically closed field of characteristic zero is an automorphism. We also construct an analytic curve in ℂ⁶ and its holomorphic bijection which is not a biholomorphism.
Nous généralisons la théorie de l’intégration motivique au cadre des schémas formels. Nous définissons et étudions l’anneau booléen des ensembles mesurables, la mesure motivique, l’intégrale motivique et nous démontrons un théorème de changement de variables pour cette intégrale.
We build on preceeding work of Serre, Esnault-Kahn-Viehweg and Kahn to establish a relation between invariants, in modulo 2 étale cohomology, attached to a tamely ramified covering of schemes with odd ramification indices. The first type of invariant is constructed using a natural quadratic form obtained from the covering. In the case of an extension of Dedekind domains, mains, this form is the square root of the inverse different equipped with the trace form. In the case of a covering of Riemann...
A broad family of involutive birational transformations of an open dense subset of onto itself is constructed explicitly. Examples with arbitrarily high complexity are presented. Construction of birational transformations such that for a fixed integer is also presented.