scholarly journals A Note on Ramification of the Galois Representation on the Fundamental Group of an Algebraic Curve, II

1995 ◽  
Vol 53 (2) ◽  
pp. 342-355 ◽  
Author(s):  
T. Oda
Keyword(s):  
Fundamental Group ◽  
Algebraic Curve ◽  
Galois Representation

On the Fundamental Group of an Algebraic Curve

1933 ◽  
Vol 55 (1/4) ◽  
pp. 255 ◽  
Author(s):  
Egbert R. Van Kampen
Keyword(s):  
Fundamental Group ◽  
Algebraic Curve

On the fundamental group of the complement of certain singular plane curves

1987 ◽  
Vol 102 (3) ◽  
pp. 453-457 ◽  
Author(s):  
András Némethi
Keyword(s):  
Projective Space ◽  
Fundamental Group ◽  
Algebraic Curve ◽  
Plane Curves ◽  
Image Position

Let C be a complex algebraic curve in the projective space ℙ2. The purpose of this paper is to calculate the fundamental group G of the complement of C in the case when C = X ∩ H1 ∩ … ∩ Hn−2, whereand Hi are generic hyperplanes (i = 1, … n − 2).

scholarly journals INTEGRAL AND ADELIC ASPECTS OF THE MUMFORD–TATE CONJECTURE

2018 ◽  
Vol 19 (3) ◽  
pp. 869-890 ◽  
Author(s):  
Anna Cadoret ◽  
Ben Moonen
Keyword(s):  
Fundamental Group ◽  
Abelian Variety ◽  
Finite Type ◽  
Galois Representation ◽  
Shimura Variety ◽  
General Statement ◽  
Tate Conjecture ◽  
Tate Module ◽  
Special Cases ◽  
Image Theorem

Let $Y$ be an abelian variety over a subfield $k\subset \mathbb{C}$ that is of finite type over $\mathbb{Q}$. We prove that if the Mumford–Tate conjecture for $Y$ is true, then also some refined integral and adelic conjectures due to Serre are true for $Y$. In particular, if a certain Hodge-maximality condition is satisfied, we obtain an adelic open image theorem for the Galois representation on the (full) Tate module of $Y$. We also obtain an (unconditional) adelic open image theorem for K3 surfaces. These results are special cases of a more general statement for the image of a natural adelic representation of the fundamental group of a Shimura variety.

The fundamental group of the complement of an algebraic curve

1974 ◽  
Vol 14 (2) ◽  
pp. 163-172 ◽  
Author(s):  
David Prill
Keyword(s):  
Fundamental Group ◽  
Algebraic Curve

Invariant groups associated with an algebraic surface

1940 ◽  
Vol 36 (4) ◽  
pp. 414-423 ◽  
Author(s):  
D. B. Scott
Keyword(s):  
Fundamental Group ◽  
Algebraic Curve ◽  
Algebraic Surface ◽  
Algebraic Surfaces ◽  
Topological Invariants ◽  
Period Matrix ◽  
Birational Transformations

Alexander (1, 2) has introduced certain topological invariants of a manifold which arise from the intersections of cycles of non-complementary dimensions, and he points out that they are not derivable from the Betti and torsion numbers, nor from the fundamental group. In the present paper we consider some topological invariants of this type on an algebraic surface, and, although we cannot define them completely, we show that they are intimately connected with the multiplications of the period matrix of the simple integrals of the first kind. We are then led to a concept which we call the “intersection group” of the surface, which is, by its definition, topologically invariant, and we show that it is also invariant under birational transformations. The proofs are based on Lefschetz's theory of cycles for an algebraic surface (4) and some simple properties of the period matrix of an algebraic curve. The results obtained here have a number of applications to the theory of ∞3 correspondences between algebraic surfaces, as we propose to show in a later paper.

Sign in / Sign up

Export Citation Format

Share Document