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The geometric Bogomolov conjecture for small genus curves
"... Abstract. The Bogomolov Conjecture is a finiteness statement about algebraic points of small height on a smooth complete curve defined over a global field. We verify an effective form of the Bogomolov Conjecture for all curves of genus at most 4 over a function field of characteristic zero. We recov ..."
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Cited by 4 (1 self)
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Abstract. The Bogomolov Conjecture is a finiteness statement about algebraic points of small height on a smooth complete curve defined over a global field. We verify an effective form of the Bogomolov Conjecture for all curves of genus at most 4 over a function field of characteristic zero. We
Strict support of canonical measures and applications to the geometric Bogomolov conjecture
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SUBVARIETIES OF ABELIAN SCHEMES OVER CONSTANT VARIETIES AND THE GEOMETRIC BOGOMOLOV CONJECTURE
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Bogomolov on tori revisited
"... Let V ⊆ Gnm ⊆ Pn be a geometrically irreducible variety which is not torsion (i. e. not a translate of a subtorus by a torsion point). For θ> 0 let V (θ) be the set of α ∈ V (Q) of Weil’s height h(α) ≤ θ. By the toric case of Bogomolov conjecture (which is a theorem of Zhang), ..."
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Cited by 1 (1 self)
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Let V ⊆ Gnm ⊆ Pn be a geometrically irreducible variety which is not torsion (i. e. not a translate of a subtorus by a torsion point). For θ> 0 let V (θ) be the set of α ∈ V (Q) of Weil’s height h(α) ≤ θ. By the toric case of Bogomolov conjecture (which is a theorem of Zhang),
Bogomolov conjecture over function fields for stable curves with only irreducible fibers
"... Abstract. Let K be a function field and C a nonisotrivial curve of genus g ≥ 2 over K. In this paper, we will show that if C has a global stable model with only geometrically irreducible fibers, then Bogomolov conjecture over function fields holds. Contents ..."
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Cited by 15 (4 self)
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Abstract. Let K be a function field and C a nonisotrivial curve of genus g ≥ 2 over K. In this paper, we will show that if C has a global stable model with only geometrically irreducible fibers, then Bogomolov conjecture over function fields holds. Contents
KOSZUL PROPERTY AND BOGOMOLOV’S CONJECTURE
, 1998
"... Let F be an arbitrary field and GF = Gal(F /F) be the Galois group of its separable algebraic closure F over it. Two conjectures about the homological properties of the group GF are widely known. First of them, the Bloch–Kato conjecture, states that for a prime number l for which F contains the lro ..."
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Cited by 8 (7 self)
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Let F be an arbitrary field and GF = Gal(F /F) be the Galois group of its separable algebraic closure F over it. Two conjectures about the homological properties of the group GF are widely known. First of them, the Bloch–Kato conjecture, states that for a prime number l for which F contains the l
§1. The Geometry Surrounding Bogomolov’s Proof
, 2015
"... Abstract. The purpose of the present paper is to expose, in substantial detail, certain remarkable similarities between interuniversal Teichmüller theory and the theory surrounding Bogomolov’s proof of the geometric version of the Szpiro Conjecture. These similarities are, in some sense, consequen ..."
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Abstract. The purpose of the present paper is to expose, in substantial detail, certain remarkable similarities between interuniversal Teichmüller theory and the theory surrounding Bogomolov’s proof of the geometric version of the Szpiro Conjecture. These similarities are, in some sense
Geometric engineering of quantum field theories
 Nucl. Phys. B497
, 1997
"... Using the recent advances in our understanding of nonperturbative aspects of type II strings we show how nontrivial exact results for N = 2 quantum field theories can be reduced to Tdualities of string theory. This is done by constructing a local geometric realization of quantum field theories to ..."
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Cited by 229 (28 self)
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Using the recent advances in our understanding of nonperturbative aspects of type II strings we show how nontrivial exact results for N = 2 quantum field theories can be reduced to Tdualities of string theory. This is done by constructing a local geometric realization of quantum field theories
The Bogomolov conjecture for totally degenerate abelian varietieties
"... Let K = k(B) be a function field of an integral projective variety B over the algebraically closed field k such that B is regular in codimension 1. The set of ..."
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Cited by 19 (4 self)
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Let K = k(B) be a function field of an integral projective variety B over the algebraically closed field k such that B is regular in codimension 1. The set of
Results 1  10
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1,562