Two-Dimensional l-Adic Representations of the Fundamental Group of a Curve Over a Finite Field and Automorphic Forms on GL(2)

1983 ◽  
Vol 105 (1) ◽  
pp. 85 ◽  
Author(s):  
V. G. Drinfeld
Keyword(s):  
Finite Field ◽  
Fundamental Group ◽  
Automorphic Forms ◽  
Two Dimensional

scholarly journals Galois representations attached to automorphic forms on over fields

2014 ◽  
Vol 150 (4) ◽  
pp. 523-567 ◽  
Author(s):  
Chung Pang Mok
Keyword(s):  
Automorphic Forms ◽  
Galois Representations ◽  
Suitable Condition ◽  
Two Dimensional ◽  
Automorphic Representations ◽  
Cuspidal Automorphic Representations ◽  
Central Characters

AbstractIn this paper we generalize the work of Harris–Soudry–Taylor and construct the compatible systems of two-dimensional Galois representations attached to cuspidal automorphic representations of cohomological type on ${\rm GL}_2$ over a CM field with a suitable condition on their central characters. We also prove a local-global compatibility statement, up to semi-simplification.

scholarly journals Abelianity Conjecture for Special Compact Kähler 3-Folds

2013 ◽  
Vol 57 (1) ◽  
pp. 55-78 ◽  
Author(s):  
Fréderic Campana ◽  
Benoît Claudon
Keyword(s):  
Fundamental Group ◽  
Ricci Curvature ◽  
Minimal Model ◽  
Classification Theory ◽  
Canonical Bundle ◽  
Two Dimensional ◽  
Basic Properties

AbstractUsing orbifold metrics of the appropriately signed Ricci curvature on orbifolds with a negative or numerically trivial canonical bundle and the two-dimensional log minimal model programme, we prove that the fundamental group of special compact Kähler 3-folds is almost abelian. This property was conjectured in all dimensions by Campana in 2004, and also for orbifolds in 2007, where the notion of specialness was introduced. We briefly recall the definition, basic properties and the role of special manifolds in classification theory.

scholarly journals Inverse monoids and immersions of 2-Complexes

2015 ◽  
Vol 25 (01n02) ◽  
pp. 301-323 ◽  
Author(s):  
John Meakin ◽  
Nóra Szakács
Keyword(s):  
Topological Space ◽  
Fundamental Group ◽  
Conjugacy Classes ◽  
Inverse Monoid ◽  
Two Dimensional ◽  
Inverse Monoids ◽  
Mild Conditions ◽  
Cw Complex ◽  
Cw Complexes

It is well known that under mild conditions on a connected topological space 𝒳, connected covers of 𝒳 may be classified via conjugacy classes of subgroups of the fundamental group of 𝒳. In this paper, we extend these results to the study of immersions into two-dimensional CW-complexes. An immersion f : 𝒟 → 𝒞 between CW-complexes is a cellular map such that each point y ∈ 𝒟 has a neighborhood U that is mapped homeomorphically onto f(U) by f. In order to classify immersions into a two-dimensional CW-complex 𝒞, we need to replace the fundamental group of 𝒞 by an appropriate inverse monoid. We show how conjugacy classes of the closed inverse submonoids of this inverse monoid may be used to classify connected immersions into the complex.

The projective fundamental group of a ℤ2-shift

1995 ◽  
Vol 15 (6) ◽  
pp. 1091-1118 ◽  
Author(s):  
William Geller ◽  
James Propp
Keyword(s):  
Topological Space ◽  
Fundamental Group ◽  
Topological Conjugacy ◽  
Fundamental Groups ◽  
Two Dimensional ◽  
Limit Group ◽  
Long Distance ◽  
Mixing Properties ◽  
Point Data ◽  
Factor Maps

AbstractWe define a new invariant for symbolic ℤ2-actions, the projective fundamental group. This invariant is the limit of an inverse system of groups, each of which is the fundamental group of a space associated with the ℤ2-action. The limit group measures a kind of long-distance order that is manifested along loops in the plane, and roughly speaking bears the same relation to the mixing properties of the ℤ2-action that π1; of a topological space bears to π0. The projective fundamental group is invariant under topological conjugacy. We calculate this invariant for several important examples of ℤ2-actions, and use it to prove non-existence of certain constant-to-one factor maps between two-dimensional subshifts. Subshifts that have the same entropy and periodic point data can have different projective fundamental groups.

AN EXACT FINITE FIELD RENORMALIZATION GROUP CALCULATION ON A TWO-DIMENSIONAL FRACTAL LATTICE

2000 ◽  
Vol 11 (02) ◽  
pp. 257-275 ◽  
Author(s):  
J. F. NYSTROM
Keyword(s):  
Renormalization Group ◽  
Finite Field ◽  
Spin System ◽  
Spin Coupling ◽  
Analysis Tool ◽  
Two Dimensional ◽  
Free Energy Surface ◽  
Fractal Lattice ◽  
Real Space Renormalization Group ◽  
Renormalization Group Calculation

A two-dimensional fractal lattice, herein referred to as the tetrahedral gasket, is used as a model for an exact two-dimensional real-space renormalization group calculation. It is shown that this Ising spin-system has exact solutions which includes a nontrivial phase transition even in the presence of a finite field. The calculation also introduces a new analysis tool, the free energy surface plot, which gives further insight into the phase diagram of the spin-system. The discussion includes comments concerning the apparent preference of the system to maintain some finite entropy, even in the presence of an extremely large spin–spin coupling.

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