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Fuchsian Subgroups of the Picard Group

Canadian Journal of Mathematics, 1976
The Picard group Γ = PSL2 (Z(i)) is the group of linear transformationswith a, b, c, d Gaussian integers.Γ is of interest both as an abstract group and in automorphic function theory [10]. In [10] Waldinger constructed a subgroup H of finite index which is a generalized free product, while in [1] Fine showed that T is a semidirect product with the ...
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Picard Groups of Rings of Coinvariants

Algebras and Representation Theory, 2007
The author extends results of \textit{A. R. Magid} [J. Pure Appl. Algebra 17, 305-311 (1980; Zbl 0437.14002)] on the Picard group of rings of invariants. He considers Doi-Hopf data \((H,A,C)\) satisfying certain conditions that entail that \(A\otimes C\), which is always an \(A\)-coring, is also a commutative associative algebra. \(G(A\otimes C)\), the
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Congruence Subgroups of the Picard Group

Canadian Journal of Mathematics, 1980
The Picard group Γ = PSL2 (Z [i]) is the group of linear fractional transformationswith ad – bc = ± 1 and a, b, c, d Gaussian integers.Γ is of interest as an abstract group and in automorphic function theory. In an earlier paper [1], a decomposition of Γ as a free product with amalgamated subgroup was given and this was utilized to investigate Fuchsian
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Picard groups for graded coalgebras

Communications in Algebra, 2000
In the theory of coalgebras, many examples of graded coalgebras appear (dual of group algebras, symmetric algebras, path coalgebras, etc). Graded coalgebras were formally introduced in [NT1] and these have also been studied in [NT1], [NT2], [DNRV] and [DNR]. The aim of this paper is to introduce some group invariants for a graded coalgebra.
J. Cuadra   +2 more
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Calculating relative Hermitian Picard groups

1995
In a series of previous papers, the authors have introduced and studied the relative hermitian Picard group of an \(R\)-algebra with involution \((A,\alpha)\) with respect to a torsion radical \(\sigma\) in \(A\)-Mod. The aim of the present paper is to give a survey on this subject, as well as to calculate the relative Picard group \(\text{Pic}_R(A ...
Reyes, M.V.   +2 more
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Picard groups of severi varieties

Communications in Algebra, 1994
We show that Severi varieties of sufficiently nodal plane curves have rational Picard group zero. The technique is to factor the natural map from the Severi variety to the moduli space of curves into a composition of fibrations each of which is well understood.
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Class Groups and Picard Groups of Orders

Proceedings of the London Mathematical Society, 1974
Fröhlich, A., Reiner, Irving, Ullom, S.
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Groupes de Picard et problèmes de Skolem. II. (Picard groups and Skolem problems. II)

1989
The author proves the following refinement of the main theorem of part I of this paper [ibid. 22, No.2, 161-179 (1989; see the preceding review)] the notation of which we preserve. Assume that R is global, i.e. arises as a localization of a ring of algebraic numbers K or as an open affine set of a smooth algebraic curve over a finite field.
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