Conditional on the Loughran-Santens conjecture, the count of Galois Heis_4-extensions of Q with |disc|≤X is predicted to grow like ½(C0+Cβ) X^{1/32}(log X)^8, with the constant a sum of two Euler products.
Malle’s conjecture and Brauer groups of stacks
9 Pith papers cite this work. Polarity classification is still indexing.
9
Pith papers citing it
abstract
We put forward a conjecture for the leading constant in Malle's conjecture on number fields of bounded discriminant, guided by stacky versions of conjectures of Batyrev-Manin, Batyrev-Tschinkel, and Peyre on rational points of bounded height on Fano varieties. A new framework for Brauer groups of stacks plays a key role in our conjecture, and we define a new notion of the unramified Brauer group of an algebraic stack.
representative citing papers
Proves Erdős-Kac type central limit theorems for the number of ramified primes in random G-extensions of number fields when G is abelian, including first examples of dependent local ramification events.
For wild-by-tame split metacyclic groups, the stringy Euler number of the quotient depends on the representation and is not always equal to the number of conjugacy classes, unlike the classical McKay case.
Neutral faithful representations of finite groups are fully classified in dimension ≤3, with a general neutrality criterion for abelian groups and a normalizer theory for gerbe morphisms that depends only on geometric type.
The étale Brauer-Manin obstruction is the only obstruction to strong approximation for the classifying stack BG of a linear algebraic group G over a number field k.
Authors conjecture an explicit leading constant for the number of number fields of bounded discriminant by transferring Manin philosophy to classifying stacks, plus related conjectures on multi-heights and local conditions.
Establishes group presentations for quotients of G_∅^T(K) in Γ-extensions and derives a random model predicting the distribution of these Galois groups over arbitrary global base fields Q.
Proves log Manin's conjecture for Campana rational curves and A1-curves on split toric varieties by combining Cox-ring moduli descriptions with Batyrev-style counting.
Survey of the homological sieve and its applications to Manin's conjecture.
citing papers explorer
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A refined Malle conjecture for Heisenberg groups
Conditional on the Loughran-Santens conjecture, the count of Galois Heis_4-extensions of Q with |disc|≤X is predicted to grow like ½(C0+Cβ) X^{1/32}(log X)^8, with the constant a sum of two Euler products.
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Erd\H{o}s-Kac theorems for discriminants of number fields
Proves Erdős-Kac type central limit theorems for the number of ramified primes in random G-extensions of number fields when G is abelian, including first examples of dependent local ramification events.
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The McKay correspondence and local heights for wild-by-tame split metacyclic groups
For wild-by-tame split metacyclic groups, the stringy Euler number of the quotient depends on the representation and is not always equal to the number of conjugacy classes, unlike the classical McKay case.
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Neutral representations in dimension $\leq 3$ and fields of moduli
Neutral faithful representations of finite groups are fully classified in dimension ≤3, with a general neutrality criterion for abelian groups and a normalizer theory for gerbe morphisms that depends only on geometric type.
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The \'{e}tale Brauer-Manin obstruction for classifying stacks
The étale Brauer-Manin obstruction is the only obstruction to strong approximation for the classifying stack BG of a linear algebraic group G over a number field k.
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The leading constant in Malle's conjecture
Authors conjecture an explicit leading constant for the number of number fields of bounded discriminant by transferring Manin philosophy to classifying stacks, plus related conjectures on multi-heights and local conditions.
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Presentations of Galois groups of unramified extensions of global fields and its predicted distribution
Establishes group presentations for quotients of G_∅^T(K) in Γ-extensions and derives a random model predicting the distribution of these Galois groups over arbitrary global base fields Q.
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Manin's conjecture for semi-integral curves and $\mathbb A^1$-connectedness
Proves log Manin's conjecture for Campana rational curves and A1-curves on split toric varieties by combining Cox-ring moduli descriptions with Batyrev-style counting.
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Homological sieve and Manin's conjecture
Survey of the homological sieve and its applications to Manin's conjecture.