Related papers: Two small remarks on Nori fundamental group scheme

In this paper we introduce the local Nori fundamental group scheme of a reduced scheme or algebraic stack over a perfect field $k$. We give particular attention to the case of fields: to any field extension $K/k$ we attach a pro-local group…

It turns out that one can read off facts about schemes up to universal homeomorphism from their Galois categories. Here we propose a first modest slate of entries in a dictionary between the geometric features of a perfectly reduced scheme…

In this note we generalize Nori's definition of the fundamental group scheme from a rational point to an arbitrary base point so that when we take $X$ to be a field $k$ and the point to be $k\subseteq \bar{k}$ we still get a non trivial…

We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…

We follow the pattern in a recent paper of Otabe [Ota15] to define an action of the \'etale fundamental group scheme $\pi^\text{et}(X)$ on the local component of the essentially finite fundamental group scheme $\pi^{\mathrm{EF}}(X)$ of…

We extend the definition of fundamental group scheme to non reduced schemes over any connected Dedekind scheme. Then we compare the fundamental group scheme of an affine scheme with that of its reduced part.

We establish a correspondence between consistent comprehension schemes and complete orthogonal factorisation systems. The comprehensive factorisation of a functor between small categories arises in this way. Similar factorisation systems…

For a map f: X -> Y of quasi-compact quasi-separated schemes, we discuss quasi-perfection, that is, the right adjoint f^\times of the derived functor Rf_* respects small direct sums. This is equivalent to the existence of a functorial…

Deformation theory is treated for locally notherian formal schemes (non necessarily smooth). The cotangent complex is defined in the derived category through the homology localization functor. The basic properties and results of a…

We introduce three notion of tameness of the Nori fundamental group scheme for a normal quasiprojective variety $X$ over an algebraically closed field. It is proved that these three notions agree if $X$ admits a smooth completion with…

Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated…

Let X be a smooth projective variety defined over an algebraically closed field k. Nori constructed a category of vector bundles on X, called essentially finite vector bundles, which is reminiscent of the category of representations of the…

Let $X$ be a fixed projective scheme which is flat over a base scheme $S$. The association taking a quasi-projective $S$-scheme $Y$ to the scheme parametrizing $S$-morphisms from $X$ to $Y$ is functorial. We prove that this functor…

Consider pairs of the form (G, N), with G a group and N \normal G, as objects of a category \PG. A morphism (G_1, N_1) \To (G_2, N_2) will be a group homomorphism f : G_1 \To G_2 such that f(N_1) \subset N_2. We introduce a functor Q : \PG…

Let $X$ be a scheme. In this text, we extend the known definitions of a topology on the set $X(R)$ of $R$-rational points from topological fields, local rings and ad\`ele rings to any ring $R$ with a topology. This definition is functorial…

We construct a wide subcategory of the category of finite association schemes with a collection of desirable properties. Our subcategory has a first isomorphism theorem analogous to that of groups. Also, standard constructions taking…

In this note, we prove that the F-fundamental group scheme is birational invariant for smooth projective varieties. We prove that the F-fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. For elliptic…

In a recent paper [3], the authors introduced a map $\mathcal{F}$ which associates a Deitmar scheme (which is defined over the field with one element, denoted by $\mathbb{F}_1$) with any given graph $\Gamma$. By base extension, a scheme…

Our main result establishes functorial desingularization of noetherian quasi-excellent schemes over $\bfQ$ with ordered boundaries. A functorial embedded desingularization of quasi-excellent schemes of characteristic zero is deduced.…

In this paper we describe the fundamental group-scheme of a proper variety fibered over an abelian variety with rationally connected fibers over an algebraically closed field. We use old and recent results for the Nori fundamental…