Chebyshev’s bias in Galois extensions of global function fields
نویسنده
چکیده
Article history: Received 18 November 2009 Revised 6 January 2011 Accepted 15 March 2011 Available online xxxx Communicated by David Goss MSC: primary 11N05 secondary 11M38, 11G05
منابع مشابه
Projective extensions of fields
A field K admits proper projective extensions, i.e. Galois extensions where the Galois group is a nontrivial projective group, unless K is separably closed or K is a pythagorean formally real field without cyclic extensions of odd degree. As a consequence, it turns out that almost all absolute Galois groups decompose as proper semidirect products. We show that each local field has a unique maxi...
متن کاملGlobal Solvably Closed Anabelian Geometry
In this paper, we study the pro-Σ anabelian geometry of hyperbolic curves, where Σ is a nonempty set of prime numbers, over Galois groups of “solvably closed extensions” of number fields — i.e., infinite extensions of number fields which have no nontrivial abelian extensions. The main results of this paper are, in essence, immediate corollaries of the following three ingredients: (a) classical ...
متن کاملNotes on Galois Theory
§1. Algebraic Extensions 2 §1.1. Field extensions 2 §1.2. Multiplicativity of degree 4 §1.3. Algebraic extensions 4 §1.4. Adjoining roots 5 §1.5. Splitting fields 5 §1.6. Algebraic closure 7 §1.7. Finite fields 9 §1.8. Composite field 9 §1.9. Exercises 10 §2. Galois Theory 11 §2.1. Separable extensions 11 §2.2. Normal extensions 13 §2.3. Main Theorem of Galois Theory 13 §2.4. Fields of invarian...
متن کاملA History of Selected Topics in Categorical Algebra I: From Galois Theory to Abstract Commutators and Internal Groupoids
This paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical Galois theory and involves generalized central extensions, commutators, and internal groupoids in Barr exact Mal’tsev and more general categories. Galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...
متن کاملGalois Towers over Non-prime Finite Fields
In this paper we construct Galois towers with good asymptotic properties over any nonprime finite field F`; i.e., we construct sequences of function fields N = (N1 ⊂ N2 ⊂ · · · ) over F` of increasing genus, such that all the extensions Ni/N1 are Galois extensions and the number of rational places of these function fields grows linearly with the genus. The limits of the towers satisfy the same ...
متن کامل