Related papers: On the homotopy exact sequence for log algebraic f…

We show exactness of the homotopy sequence for the logarithmic fundamental group in the case of log smooth, finitely presented, proper and saturated morphisms of fs log schemes over a field. This generalizes earlier results of Hoshi in the…

In this note, we prove that the homotopy sequence of the algebraic fundamental group is exact if the base field is of characteristic 0.

In this article we prove exactness of the homotopy sequence of overconvergent $p$-adic fundamental groups for a smooth and projective morphism in characteristic $p$. We do so by first proving a corresponding result for rigid analytic…

The goal of this paper is to first define a Hodge theoretic fundamental group for smooth connected complex algebraic varieties and then prove and study a right exact sequence of Hodge theoretic fundamental groups associated to a smooth…

A separable, proper morphism of varieties with geometrically connected fibers induces a homotopy exact sequence relating the \'etale fundamental groups of source, target and fiber. Extending work of dos Santos, we prove the existence of an…

Consider a morphism between connected locally Noetherian normal schemes. In this paper, we discuss when the sequence of the etale fundamental groups associated to the morphism is exact. Moreover, we give a characterization of when the…

Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of 'homotopical exactness', appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be…

We study the homotopy groups of complements to reducible divisors on non-singular projective varieties with ample components and isolated non normal crossings. We prove a vanishing theorem generalizing conditions for commutativity of the…

In homotopy theory, exact sequences and spectral sequences consist of groups and pointed sets, linked by actions. We prove that the theory of such exact and spectral sequences can be established in a categorical setting which is based on…

Unlike Grothendieck's \'etale fundamental group, Nori's fundamental group does not fulfill the homotopy exact sequence in general. We give necessary and sufficient conditions which force exactness of the sequence.

In this paper, we prove compatibilities of various definitions of relatively unipotent log de Rham fundamental groups for certain proper log smooth integral morphisms of fine log schemes of characteristic zero. Our proofs are purely…

In the paper we describe the almost split sequences in the homotopy category of perfect complexes over a gentle algebra.

Crossed complexes are shown to have an algebra sufficiently rich to model the geometric inductive definition of simplices, and so to give a purely algebraic proof of the Homotopy Addition Lemma (HAL) for the boundary of a simplex. This…

In this paper, we investigate the necessary sufficient conditions for the exactness of the homotopy sequence of Nori's fundamental group and apply these to various special situations to regain some classical theorems and give a counter…

In this article we give two applications of the spectral sequence of the log Hodge-Witt cohomology of a proper SNCL scheme over the log point of a perfect field of characterisitic $p>0$.

Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.

We compare the log motivic stable homotopy category and the usual motivic stable homotopy category over a perfect field admitting resolution of singularities. As a consequence, we show that the log motivic stable homotopy groups are…

In this paper, we construct a seven-term exact sequence involving the cohomology groups of a group extension. Although the existence of such a sequence can be derived using spectral sequence arguments, there is little knowledge about some…

We show that the category of log homotopy types is a full subcategory of a category of homotopy types with modulus.

We propose a method for constructing cohomology theories of logarithmic schemes with strict normal crossing boundaries by employing techniques from logarithmic motivic homotopy theory over $\mathbb{F}_1$. This method recovers the K-theory…