On ramification index of composition of complete discrete valuation fields

2020 ◽  
Vol 130 (1) ◽  
Author(s):  
Pasupulati Sunil Kumar
Keyword(s):  
Ramification Index

scholarly journals Ramification Theory for Extensions of Degree p. II

1972 ◽  
Vol 46 ◽  
pp. 97-109
Author(s):  
Susan Williamson
Keyword(s):  
Valuation Ring ◽  
Quotient Field ◽  
Root Of Unity ◽  
Ramification Index ◽  
Ramification Theory ◽  
Rank One ◽  
The Absolute

Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.

scholarly journals On the determination of the ramification index in Clifford's theorem

1988 ◽  
Vol 31 (3) ◽  
pp. 469-474
Author(s):  
Robert W. van der Waall
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Ramification Index ◽  
A Finite Group

Let K be a field, G a finite group, V a (right) KG-module. If H is a subgroup of G, then, restricting the action of G on V to H, V is also a KH-module. Notation: VH.Suppose N is a normal subgroup of G. The KN-module VN is not irreducible in general, even when V is irreducible as KG-module. A part of the well-known theorem of A. H. Clifford [1, V.17.3] yields the following.

Local Bounds for Torsion Points on Abelian Varieties

2008 ◽  
Vol 60 (3) ◽  
pp. 532-555 ◽  
Author(s):  
Pete L. Clark ◽  
Xavier Xarles
Keyword(s):  
Abelian Varieties ◽  
Residue Field ◽  
Rational Numbers ◽  
Abelian Surface ◽  
Torsion Subgroup ◽  
Good Reduction ◽  
Torsion Points ◽  
Ramification Index ◽  
Numerical Invariants ◽  
Split Torus

AbstractWe say that an abelian variety over a p-adic field K has anisotropic reduction (AR) if the special fiber of its Néronminimal model does not contain a nontrivial split torus. This includes all abelian varieties with potentially good reduction and, in particular, those with complex or quaternionic multiplication. We give a bound for the size of the K-rational torsion subgroup of a g-dimensional AR variety depending only on g and the numerical invariants of K (the absolute ramification index and the cardinality of the residue field). Applying these bounds to abelian varieties over a number field with everywhere locally anisotropic reduction, we get bounds which, as a function of g, are close to optimal. In particular, we determine the possible cardinalities of the torsion subgroup of an AR abelian surface over the rational numbers, up to a set of 11 values which are not known to occur. The largest such value is 72.

Enumerating extensions of (π)-adic fields with given invariants

2017 ◽  
Vol 13 (08) ◽  
pp. 2007-2038
Author(s):  
Sebastian Pauli ◽  
Brian Sinclair
Keyword(s):  
Minimal Set ◽  
Ramification Index

We give an algorithm that constructs a minimal set of polynomials defining all extensions of a [Formula: see text]-adic field with given inertia degree, ramification index, discriminant, ramification polygon, and residual polynomials of the segments of the ramification polygon.

scholarly journals Ramification index and multiplicity

1963 ◽  
Vol 7 (4) ◽  
pp. 566-581 ◽  
Author(s):  
M. Auslander ◽  
D. S. RIM
Keyword(s):  
Ramification Index

scholarly journals ON THE SPACE OF HARMONIC 2-SPHERES IN CP2

1996 ◽  
Vol 07 (02) ◽  
pp. 211-225 ◽  
Author(s):  
L. LEMAIRE ◽  
J.C. WOOD
Keyword(s):  
Harmonic Maps ◽  
Holomorphic Maps ◽  
Ramification Index ◽  
Gauss Transform ◽  
Complex Projective

Carrying further the work of T.A. Crawford, we show that each component of the space of harmonic maps from the 2-sphere to complex projective 2-space of degree d and energy 4πE is a smooth closed submanifold of the space of all Cj maps (j≥2). We achieve this by showing that the Gauss transform which relates them to spaces of holomorphic maps of given degree and ramification index is smooth and has injective differential.

scholarly journals Regular formal modules in local fields and irregularly degree

2020 ◽  
Vol 65 (4) ◽  
pp. 588-596
Author(s):  
Natalya K. Vlaskina ◽  
◽  
Sergei V. Vostokov ◽  
Petr N. Pital’ ◽  
Aleksey E. Tsybyshiev ◽  
...  
Keyword(s):  
Positive Integer ◽  
Local Field ◽  
Sufficient Conditions ◽  
Formal Group ◽  
Necessary And Sufficient Conditions ◽  
Local Fields ◽  
Ramification Index ◽  
Necessary And Sufficient ◽  
Primitive Roots

In this paper we investigate the irregular degree of finite not ramified local field extantions with respect to a polynomial formal group and in the multiplicative case. There was found necessary and sufficient conditions for the existence of primitive roots of ps power from 1 and (endomorphism [ps]Fm) in L-th unramified extension of the local field K (for all positive integer s). These conditions depend only on the ramification index of the maximal abelian subextension of the field K Ka/Qp.

The Schur Subgroup of a p-Adic Field

1979 ◽  
Vol 31 (2) ◽  
pp. 300-303
Author(s):  
Eugene Spiegel ◽  
Allan Trojan
Keyword(s):  
Finite Group ◽  
Simple Group ◽  
Group Algebras ◽  
Brauer Group ◽  
Ramification Index ◽  
Simple Component ◽  
Image Position ◽  
Cyclotomic Algebras ◽  
A Finite Group ◽  
Tame Ramification

Let K be a field. The Schur subgroup, S(K), of the Brauer group, B(K), consists of all classes [△] in B(K) some representative of which is a simple component of one of the semi-simple group algebras, KG, where G is a finite group such that char K ∤ G. Yamada ([11], p. 46) has characterized S(K) for all finite extensions of the p-adic number field, Qp. If p is odd, [△] ∈ S(K) if and only ifwhere c is the tame ramification index of k/Qp, k the maximal cyclotomic subfield of K, and s = ((p – 1)/c, [K : k]). invp △ is the Hasse invariant. Yamada showed this by proving first that S(K) is the group of classes containing cyclotomic algebras and then determining the invariants of such algebras.

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