scholarly journals The inverse Galois problem and rational points on moduli spaces

1991 ◽  
Vol 290 (1) ◽  
pp. 771-800 ◽  
Author(s):  
Michael D. Fried ◽  
Helmut V�lklein
Keyword(s):  
Moduli Spaces ◽  
Rational Points ◽  
Inverse Galois Problem

scholarly journals A heuristic for the distribution of point counts for random curves over a finite field

2015 ◽  
Vol 373 (2040) ◽  
pp. 20140310 ◽  
Author(s):  
Jeffrey D. Achter ◽  
Daniel Erman ◽  
Kiran S. Kedlaya ◽  
Melanie Matchett Wood ◽  
David Zureick-Brown
Keyword(s):  
Finite Field ◽  
Poisson Distribution ◽  
Moduli Spaces ◽  
Algebraic Curve ◽  
Rational Points ◽  
Random Curves ◽  
Point Counts ◽  
Moduli Spaces Of Curves ◽  
Large Genus

How many rational points are there on a random algebraic curve of large genus g over a given finite field ? We propose a heuristic for this question motivated by a (now proven) conjecture of Mumford on the cohomology of moduli spaces of curves; this heuristic suggests a Poisson distribution with mean q +1+1/( q −1). We prove a weaker version of this statement in which g and q tend to infinity, with q much larger than g .

scholarly journals Rational points of quiver moduli spaces

2020 ◽  
Vol 70 (3) ◽  
pp. 1259-1305
Author(s):  
Victoria Hoskins ◽  
Florent Schaffhauser
Keyword(s):  
Moduli Spaces ◽  
Rational Points

scholarly journals On rational points in CFT moduli spaces

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Nathan Benjamin ◽  
Christoph A. Keller ◽  
Hirosi Ooguri ◽  
Ida G. Zadeh
Keyword(s):  
Perturbation Theory ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Sigma Model ◽  
Rational Points ◽  
Target Space ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field

Abstract Motivated by the search for rational points in moduli spaces of two-dimensional conformal field theories, we investigate how points with enhanced symmetry algebras are distributed there. We first study the bosonic sigma-model with S1 target space in detail and uncover hitherto unknown features. We find for instance that the vanishing of the twist gap, though true for the S1 example, does not automatically follow from enhanced symmetry points being dense in the moduli space. We then explore the supersymmetric sigma-model on K3 by perturbing away from the torus orbifold locus. Though we do not reach a definite conclusion on the distribution of enhanced symmetry points in the K3 moduli space, we make several observations on how chiral currents can emerge and disappear under conformal perturbation theory.

Geometry and Physics: Volume II

2018 ◽  
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Geometric Analysis ◽  
Mathematical Physics ◽  
Poisson Geometry ◽  
Special Holonomy ◽  
Low Dimensional Topology ◽  
Generalized Complex Structures ◽  
Wide Range ◽  
Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

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