相关论文: Invariance of the tame fundamental group under bas…

We show that the fundamental groupoid~\(\Pi_1(X)\) of a locally path connected semilocally simply connected space~\(X\) can be equipped with a \emph{natural} topology so that it becomes a topological groupoid; we also justify the necessity…

Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…

We describe a new basis of the ring of quasi-symmetric coinvariants, which is stable by the natural reversal of the set of variables. The indexing set is the set of triangulations of a regular polygon, instead of the set of Dyck paths used…

For a locally path connected topological space, the topological fundamental group is discrete if and only if the space is semilocally simply-connected. While functoriality of the topological fundamental group for arbitrary topological…

It is proved that the tame automorphism group of a differential polynomial algebra $k\{x,y\}$ over a field $k$ of characteristic $0$ in two variables $x,y$ with $m$ commuting derivations $\delta_1, \ldots, \delta_m$ is a free product with…

We describe a set of defining relations of the tame automorphism group TA_3(F) of the polynomial algebra F[x_1,x_2,x_3] in variables x_1,x_2,x_3 over an arbitrary field F of characteristic 0.

In this article we prove that the numerical Grothendieck group of every smooth proper dg category is invariant under primary field extensions, and also that the mod-n algebraic K-theory of every dg category is invariant under extensions of…

We show that the algebraic fundamental group of a smooth projective curve over a finite field admits a finite topological presentation where the number of relations does not exceed the number of generators.

We establish the correspondence between tame harmonic bundles and $\mu_L$-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for $\mu_L$-stable parabolic Higgs bundles.…

We show that the fundamental group of every enumeratively rationally connected closed symplectic manifold is finite. In other words, if a closed symplectic manifold has a non-zero Gromov-Witten invariant with two point insertions, then it…

We consider the algebra of invariants of $d$-tuples of $n\times n$ matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic $p$ different from two. It is well-known that this…

As is well known, the Lefschetz theorems for the \'etale fundamental group of SGA1 do not hold. We fill a small gap in the literature showing they do for tame coverings. Let $X$ be a regular projective variety over a field $k$, and let…

We show that the change of basis matrices of a set of $m$ bases of a finite vector space is a connected groupoid of order $m^2$. We define a general method to express the elements of change of basis matrices as algebraic expressions using…

Let $(R,\mathfrak{m}, k)$ be a strictly local normal $k$-domain of positive characteristic and $P$ be a prime divisor on $X=\text{Spec } R$. We study the Galois category of finite covers over $X$ that are at worst tamely ramified over $P$…

The classification of equivariant toroidal embeddings of a reductive group over an algebraically closed field is combinatorial and does not depend on the characteristic of the base field. This suggests that there should exist ``universal''…

Let X be a smooth variety over a field k, and l be a prime number invertible in k. We study the (\'etale) unramified H^3 of X with coefficients Q_l/Z_l(2) in the style of Colliot-Th\'el\`ene and Voisin. If k is separably closed, finite or…

We show that the natural algebraic structure of the singular chains on a path connected topological space determines the fundamental group functorially. Moreover, we describe a notion of weak equivalence for the relevant algebraic structure…

We study the relationship between the positivity property in a rank 2 cluster algebra, and the property of such an algebra to be tame. More precisely, we show that a rank 2 cluster algebra has a basis of indecomposable positive elements if…

Given an algebraic stack, we compare its Nori fundamental group with that of its coarse moduli space. We also study conditions under which the stack can be uniformized by an algebraic space.

It is well known that all torsors under an affine algebraic group over an algebraically closed field are trivial. We note that under suitable conditions this also holds if the the group is not necessarily of finite type. This has an…