Related papers: Torsion in 1-cusped Picard modular groups

In this paper, for every prime $p$ and every $0\le n\le \infty$, we classify the structure of the torsion subgroup of the group of $\mathbb{Q}_p(\mu_{p^n})$-rational points of elliptic curves over $\mathbb{Q}_p$ with good reduction, where…

To a symmetric, relatively ample line bundle on an abelian scheme one can associate a linear combination of the determinant bundle and the relative canonical bundle, which is a torsion element in the Picard group of the base. We improve the…

We develop pivotal and spherical versions of graded extension theory. We define the corresponding analogues of Brauer-Picard $2$-categorical groups and realize them as fixed points of natural $\mathbb{Z}$ and $\mathbb{Z}/2\mathbb{Z}$…

We provide new tools for the calculation of the torsion in the cohomology of congruence subgroups in the Bianchi groups : An algorithm for finding particularly useful fundamental domains, and an analysis of the equivariant spectral sequence…

Let $S$ be a certain affine algebraic surface over $\mathbb{Q}$ such that it admits a regular map to $\mathbb{A}^2/\mathbb{Q}$. We show that any non-trivial torsion line bundle in the relative Picard group $Pic^0\left(S/\mathbb{A}^2\right)$…

In this paper we introduce a common framework for describing the topological part of the Baum-Connes conjecture for a wide class of groups. We compute the Bredon homology for groups with aspherical presentation, one-relator quotients of…

We compute the Picard group of the moduli stack of smooth curves of genus $g$ for $3\leq g\leq 5$, using methods of equivariant intersection theory. We base our proof on the computation of some relations in the integral Chow ring of certain…

We introduce the Picard group of corings. We extend the well-known exact sequence from algebras and coalgebras over fields to corings. We extend the Aut-Pic property to corings and we give some new examples of corings having this property.…

In this paper we study the embedded topology of reducible plane curves having a smooth irreducible component. In previous studies, the relation between the topology and certain torsion classes in the Picard group of degree zero of the…

Let S be a locally noetherian regular scheme. We compute the units-Picard complex of a reductive S-group scheme G in terms of the dual algebraic fundamental complex of G. To do so, we establish a units-Picard-Brauer exact sequence for a…

We construct a family of plane curves as pull-backs of a conic for abelian coverings of P^2. If the conic is tangent to the ramification lines one obtains a family of curves of degree 2n with 3n singularities of type A_{n-1}. We calculate…

Let $\mathcal{A}$ be an abelian length category containing a $d$-cluster tilting subcategory $\mathcal{M}$. We prove that a subcategory of $\mathcal{M}$ is a $d$-torsion class if and only if it is closed under $d$-extensions and…

Let $\Gamma$ be a torsion free lattice in $G = \PGL(n+1,\FF)$, where $n\ge 1$ and $\FF$ is a non-archimedean local field. Then $\Gamma$ acts on the Furstenberg boundary $G/P$, where $P$ is a minimal parabolic subgroup of $G$. The identity…

We compute the Picard group $ Pic(A_q) $ of the noncommutative algebraic 2-torus $A_q$, describe its action on the space $ R(A_q) $ of isomorphism classes of rk 1 projective modules and classify the algebras Morita equivalent to $ A_q $.…

We study the Picard groups of moduli spaces of smooth complex projective curves that have a group of automorphisms with a prescribed topological action. One of our main tools is the theory of symmetric mapping class groups. In the first…

We study the Picard groups of moduli spaces in positive characteristics and we give a "$p$-adic" proof that the Picard group of moduli of vector bundles of fixed determinant is isomorphic to the group of integers. Along the way we prove…

We start with $n$-torsions in the Jacobian of an $m$-gonal curve and produce $n$-torsions in the class group of certain number field $K$.

We use the description of the Picard modular surface for discriminant $-3$ as a moduli space of curves of genus $3$ to generate all vector-valued Picard modular forms from bi-covariants for the action of ${GL}_2$ on the space of pairs of…

We obtain an explicit upper bound on the torsion of the Picard group of the forms of the affine line and their regular completions. We also obtain a sufficient condition for the Picard group of the forms of the affine line to be non trivial…

Nous calculons le groupe de Picard de l'espace des modules $\Theta_{\planp}(d)$ des th\^eta-caract\'eristiques des courbes planes (non forc\'ement lisses) de degr\'e $d$. Nous montrons que pour $d\ge 6$, le groupe de Picard de la composante…