An Effective Schmidt’s Subspace Theorem for Projective Varieties Over Function Fields

2012 ◽  
Vol 2012 (3) ◽  
pp. 651-684
Author(s):  
Min Ru ◽  
Julie Tzu-Yueh Wang
Keyword(s):  
Function Fields ◽  
Projective Varieties ◽  
Subspace Theorem

A SIMPLE PROOF OF CHEBOTAREV’S DENSITY THEOREM OVER FINITE FIELDS

2018 ◽  
Vol 98 (2) ◽  
pp. 196-202
Author(s):  
STEVE MEAGHER
Keyword(s):  
Conjugacy Class ◽  
Finite Fields ◽  
Simple Proof ◽  
Function Fields ◽  
Rational Points ◽  
Density Theorem ◽  
Chebotarev Density Theorem ◽  
Projective Varieties

We present a simple proof of the Chebotarev density theorem for finite morphisms of quasi-projective varieties over finite fields following an idea of Fried and Kosters for function fields. The key idea is to interpret the number of rational points with a given Frobenius conjugacy class as the number of rational points of a twisted variety, which is then bounded by the Lang–Weil estimates.

scholarly journals Rational points on abelian varieties over function fields and Prym varieties

2020 ◽  
Author(s):  
Abolfazl Mohajer
Keyword(s):  
Structure Theorem ◽  
Function Fields ◽  
Abelian Varieties ◽  
High Rank ◽  
Prym Variety ◽  
Projective Varieties ◽  
Prym Varieties ◽  
Weil Group ◽  
Galois Covers ◽  
Smooth Projective Varieties

AbstractIn this paper, using a generalization of the notion of Prym variety for covers of projective varieties, we prove a structure theorem for the Mordell–Weil group of abelian varieties over function fields that are twists of abelian varieties by Galois covers of smooth projective varieties. In particular, the results we obtain contribute to the construction of Jacobians of high rank.

scholarly journals An effective Schmidt's subspace theorem for non-linear forms over function fields

2007 ◽  
Vol 125 (1) ◽  
pp. 210-228 ◽  
Author(s):  
Ta Thi Hoai An ◽  
Julie Tzu-Yueh Wang
Keyword(s):  
Function Fields ◽  
Linear Forms ◽  
Subspace Theorem ◽  
Non Linear

Cohomological Conditions on Endomorphisms of Projective Varieties

2017 ◽  
Vol 145 (3) ◽  
pp. 449-468 ◽  
Author(s):  
Holly Krieger ◽  
Paul Reschke
Keyword(s):  
Projective Varieties

scholarly journals The Kodaira Problem for Kähler Spaces with Vanishing First Chern Class

2021 ◽  
Vol 9 ◽  
Author(s):  
Patrick Graf ◽  
Martin Schwald
Keyword(s):  
Chern Class ◽  
Cohomology Group ◽  
Canonical Bundle ◽  
Deformation Space ◽  
Projective Varieties ◽  
Quotient Singularities ◽  
Finite Quotient ◽  
First Chern Class ◽  
Small Deformations

Abstract Let X be a normal compact Kähler space with klt singularities and torsion canonical bundle. We show that X admits arbitrarily small deformations that are projective varieties if its locally trivial deformation space is smooth. We then prove that this unobstructedness assumption holds in at least three cases: if X has toroidal singularities, if X has finite quotient singularities and if the cohomology group ${\mathrm {H}^{2} \!\left ( X, {\mathscr {T}_{X}} \right )}$ vanishes.

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