Finiteness theorems for algebraic cycles of small codimension on quadric...
AbstractWe obtain finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves over perfect fields. For example, if k is finitely generated over ℚ and X→ C is a...
View ArticleFlasque resolutions of reductive group schemes
AbstractWe generalize Colliot-Thélène’s construction of flasque resolutions of reductive group schemes over a field to a broad class of base schemes.
View ArticleAbelian class groups of reductive group schemes
AbstractWe introduce the abelian class group Cab (G) of a reductive group scheme G over a ring A of arithmetical interest and study some of its basic properties. For example, we show that if the...
View ArticleThe algebraic fundamental group of a reductive group scheme over an arbitrary...
AbstractWe define the algebraic fundamental group π1(G) of a reductive group scheme G over an arbitrary non-empty base scheme and show that the resulting functor G↦ π1(G) is exact.
View ArticleGalois sets of connected components and Weil restriction
AbstractLet k be a field, A a finite k-algebra and X a smooth A-scheme. We describe the Galois set of connected components of the Weil restriction \(\mathfrak {R}_{A/ k}(X)\) in terms of the sets of...
View ArticleOn the group of units and the Picard group of a product
AbstractLet S be a reduced scheme and let \(f:X\rightarrow S\) and \(g:Y\rightarrow S\) be faithfully flat morphisms locally of finite presentation with reduced and connected maximal geometric fibers....
View ArticleThe Greenberg functor revisited
AbstractWe extend Greenberg’s original construction to arbitrary schemes over (certain types of) local artinian rings. We then establish a number of properties of the extended functor and determine,...
View ArticleThe Greenberg Functor is Site Cocontinuous
AbstractIn this paper we show that it is possible to define a topology on the category of formal schemes over a ring of p-adic integers such that the left adjoint of the Greenberg Transform is a site...
View ArticleEQUIVARIANT MODELS OF SPHERICAL VARIETIES
AbstractLet G be a connected semisimple group over an algebraically closed field k of characteristic 0. Let Y = G/H be a spherical homogeneous space of G, and let Y′ be a spherical embedding of Y. Let...
View Article
