Related papers: On Nori's Fundamental Group Scheme

We propose the notion of partial resolution of a ring, which is by definition the endomorphism ring of a certain generator of the given ring. We prove that the singularity category of the partial resolution is a quotient of the singularity…

The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…

In this article, we study the log-scheme theoretic version of the Nori fundamental group scheme. Similar to the classical Nori fundamental group scheme, the log Nori fundamental group scheme classifies torsors on log flat topology. We also…

In \cite{armstrong}, M. Armstrong proved a beautiful result describing fundamental groups of quotient spaces. In this paper we prove an analogue of Armstrong's theorem in the setting of $F$-divided \cite{dS07} and essentially finite…

We give a condition that ensures that a fibered category over a field admits a universal morphism to a profinite gerbe. This fundamental gerbe generalizes both Nori's fundamental group scheme and Deligne's relative fundamental groupoid.…

Consider an exact category in the sense of Quillen. Assume that in this category every morphism has a kernel and that every kernel is an inflation. In their seminal 1982 paper, Beilinson, Bernstein and Deligne consider in this setting 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 show that the quotient of a Hom-finite triangulated category C by the kernel of the functor Hom(T, -), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admit a calculus of left…

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…

We study properties of a category after quotienting out a suitable chosen group of isomorphisms on each object. Coproducts in the original category are described in its quotient by our new weaker notion of a 'phased coproduct'. We examine…

For $X$ a complete, reduced, geometrically connected scheme over a perfect field of characteristic $p>0$, we analyze the decomposition of Nori's fundamental group scheme into its local and \'etale parts and raise the question of the…

We introduce the notion of algebraic cogroup over a subfield $k$ of the complex numbers, and use it to prove that every Nori motive over $k$ is isomorphic to a quotient of a motive of the form $H^n(X, Y)(i)$.

In this paper we introduce the notion of (pointed) prenormal category, modelled after regular categories, but with the key notions of coequaliser and kernel pair replaced by those of cokernel and kernel. This framework provides a natural…

For a rigid tensor abelian category $T$ over a field $k$ we introduce a notion of a normal quotient $q:T\to Q$. In case $T$ is a Tannaka category, our notion is equivalent to Milne's notion of a normal quotient. More precisely, if $T$ is…

This thesis provides a partial answer to a question posed by Greg Kuperberg in q-alg/9712003 and again by Justin Roberts as problem 12.18 in "Problems on invariants of knots and 3-manifolds", math.GT/0406190, essentially: "Can one describe…

We explicitly describe the Cartier dual of the $l$-th Frobenius kernel $N_l$ of the deformation group scheme, which deforms the additive group scheme to the multiplicative group scheme. Then the Cartier dual of $N_l$ is given by a certain…

The quotient of a triangulated category modulo a subcategory was defined by Verdier. Motivated by the failure of the telescope conjecture, we introduce a new type of quotients for any triangulated category which generalizes Verdier's…

Let $(X ,x_0)$ be a pointed smooth proper variety defined over an algebraically closed field. The Albanese morphism for $(X ,x_0)$ produces a homomorphism from the abelianization of the $F$-divided fundamental group scheme of $X$ to the…

We show that the representation category of the quantum group of a non-degenerate bilinear form is monoidally equivalent to the representation category of the quantum group SL_q(2), for a well chosen non-zero parameter q. The main…

Let $n \geq 2$. We introduce the notion of $n$-representations of quivers, and we explicitly provide concrete examples of $2$-representations of quivers. We establish the categories of $n$-representations and investigate kernels and…