On number fields with given ramification

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Number of Linear Series on Curves with given Ramification

We use Eisenbud and Harris’ theory of limit linear series (1986) to show that for a general smooth curve of genus g in characteristic 0, with general points Pi and indices ei such that P i(ei − 1) = 2d − 2− g, G 1 d (C, {(Pi, ei)}i) is made up of reduced points. We give a formula for the number of points, showing that it agrees with various known special cases. We also conjecture a correspondin...

متن کامل

Extensions of Number Fields with Wild Ramification of Bounded Depth

Fix a prime number p, a number field K, and a finite set S of primes of K. Let Sp be the set of all primes of K of residue characteristic p. Inside a fixed algebraic closure K of K, let KS be the maximal p-extension (Galois extension with pro-p Galois group) of K unramified outside S, and put GS = Gal(KS/K). The study of these “fundamental groups” is governed by a dichotomy between the tame (S∩...

متن کامل

Nilpotent Extensions of Number Fields with Bounded Ramification

We study a variant of the inverse problem of Galois theory and Abhyankar’s conjecture. If p is an odd rational prime and G is a finite p-group generated by s elements, s minimal, does there exist a normal extension L/Q such that Gal (L/Q) ∼= G with at most s rational primes that ramify in L? Given a nilpotent group of odd order G with s generators, we obtain a Galois extension L/Q with precisel...

متن کامل

Ramification of Local Fields with Imperfect Residue Fields II

In [1], a filtration by ramification groups and its logarithmic version are defined on the absolute Galois group of a complete discrete valuation field without assuming that the residue field is perfect. In this paper, we study the graded pieces of these filtrations and show that they are abelian except possibly in the absolutely unramified and non-logarithmic case. 2000 Mathematics Subject Cla...

متن کامل

Ramification of local fields with imperfect residue fields I

Let K be a complete discrete valuation field, and let G be the Galois group of a separable closure Ω. Classically the ramification filtration of G is defined in the case where the residue field of K is perfect ([5], Chapter IV). In this paper, we define without any assumption on the residue field, two ramification filtrations of G and study some of their properties. Our first filtration, (G)a∈Q...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Compositio Mathematica

سال: 2007

ISSN: 0010-437X,1570-5846

DOI: 10.1112/s0010437x07003132