共查询到20条相似文献,搜索用时 46 毫秒
1.
M. Somekawa 《K-Theory》1990,4(2):105-119
In this paper we define and study a Milnor K-group attached to a finite family of semi-Abelian varieties over a field, which is a generalization of the usual Milnor K-group. Using this group, we generalize the work of Bloch. 相似文献
2.
We show that if L/
K is a degree p
extension of number fields which is wildly ramified at a prime ${\frak p}$ of
K of residue characteristic
p, then the ramification groups of ${\frak p}$
(in the splitting field of L over
K) are uniquely determined by the
${\frak p}$-adic valuation of the discriminant of L
/K.Received: 3 July 2002 相似文献
3.
Shin Hattori 《Journal of Number Theory》2008,128(5):1091-1108
In this paper, for a complete discrete valuation field K of mixed characteristic (0,p) and a finite flat group scheme G of p-power order over OK, we determine the tame characters appearing in the Galois representation in terms of the ramification theory of Abbes and Saito, without any restriction on the absolute ramification index of K or the embedding dimension of G. 相似文献
4.
Suppose G is a semi-direct product of the form Z/pn?Z/m where p is prime and m is relatively prime to p. Suppose K is a complete discrete valuation field of characteristic p>0 with algebraically closed residue field. The main result states necessary and sufficient conditions on the ramification filtrations that occur for wildly ramified G-Galois extensions of K. In addition, we prove that there exists a parameter space for G-Galois extensions of K with given ramification filtration, and we calculate its dimension in terms of the ramification filtration. We provide explicit equations for wild cyclic extensions of K of degree p3. 相似文献
5.
Takao Yamazaki 《Compositio Mathematica》1998,112(2):127-145
We study a ramification theory for a division algebra D of the following type: The center of D is a complete discrete valuation field K with the imperfect residue field F of certain type, and the residue algebra of D is commutative and purely inseparable over F. Using Swan conductors of the corresponding element of Br(K), we define -function of D/K, and it describe the action of the reduced norm map on the filtration of D-. We also gives a relation among the Swan conductors and the ramification number of D, which is defined by the commutator group of D-. 相似文献
6.
The paper is devoted to classification of finite abelian extensions L/K which satisfy the condition [L:K]|D
L/K. Here K is a complete discretely valued field of characteristic 0 with an arbitrary residue field of prime characteristic p, D
L/K is the different of L/K. This condition means that the depth of ramification in L/K has its almost maximal value. The condition appeared to play an important role in the study of additive Galois modules associated with the extension L/K. The study is based on the use of the notion of independently ramified extensions, introduced by the authors. Two principal theorems are proven, describing almost maximally ramified extensions in the cases when the absolute ramification index e is (resp. is not) divisible by p-1. Bibliography: 7 titles. 相似文献
7.
Ramification in complete discrete valuation fields is studied. For the case of a perfect residue field, there is a well-developed theory of ramification groups. Hyodo introduced the concept of ramification depth associated with the different of an extension and obtained an inequality that combines the concept of ramification depth in a degree p2 cyclotomic extension with the concept of ramification depth in a degree p subextension. The paper gives a detailed consideration of the structure of degree p2 extensions that can be obtained by a composite of two degree p extensions. In this case, it is not required that the residue field be perfect. Using the concepts of wild and ferocious extensions and the defect of the main unit, degree p2 extensions are classified and more accurate estimates for the ramification depth are obtained. In a number of cases, exact formulas for ramification depth are presented. 相似文献
8.
Shin Hattori 《Journal of Number Theory》2006,118(2):145-154
In this paper, we analyze ramification in the sense of Abbes-Saito of a finite flat group scheme over the ring of integers of a complete discrete valuation field of mixed characteristic (0,p). We deduce that its Galois representation depends only on its reduction modulo explicitly computed p-power. We also give a new proof of a theorem of Fontaine on ramification of a finite flat Galois representation, and extend it to the case where the residue field may be imperfect. 相似文献
9.
Heinz Wähling 《Journal of Geometry》1988,31(1-2):194-201
It is shown that every locally compact, disconnected nearfield (F,) possesses a non-archimedean, discrete valuation ¦ ¦, which induces . The valuation nearringR of ¦ ¦ only has one maximal idealP, and the quotient groupR/P is finite. If the kernelK ofF is infinite and ifE is an infinite subfield ofK, thenR/P may be considered as a right vector space over the residue field of (E, ¦ ¦). Based on this assumption the ramification index and the residual degree are introduced and studied.
Herrn Professor Helmut Karzel zum 60. Geburtstag 相似文献
Herrn Professor Helmut Karzel zum 60. Geburtstag 相似文献
10.
Moritz Kerz 《Inventiones Mathematicae》2009,175(1):1-33
We prove that the n-th Milnor K-group of an essentially smooth local ring over an infinite field coincides with the (n,n)-motivic cohomology of the ring. This implies Levine’s generalized Bloch–Kato conjecture. 相似文献
11.
Tong Liu 《Journal of Number Theory》2007,126(2):155-184
Let R be a complete discrete valuation ring of mixed characteristic (0,p) with perfect residue field, K the fraction field of R. Suppose G is a Barsotti-Tate group (p-divisible group) defined over K which acquires good reduction over a finite extension K′ of K. We prove that there exists a constant c?2 which depends on the absolute ramification index e(K′/Qp) and the height of G such that G has good reduction over K if and only if G[pc] can be extended to a finite flat group scheme over R. For abelian varieties with potentially good reduction, this result generalizes Grothendieck's “p-adic Néron-Ogg-Shafarevich criterion” to finite level. We use methods that can be generalized to study semi-stable p-adic Galois representations with general Hodge-Tate weights, and in particular leads to a proof of a conjecture of Fontaine and gives a constant c as above that is independent of the height of G. 相似文献
12.
The aim of this note is to give a simplified proof of the surjectivity of the natural Milnor–Chow homomorphism between Milnor K-theory and higher Chow groups for essentially smooth (semi-)local k-algebras A with infinite residue fields. It implies the exactness of the Gersten resolution for Milnor K-theory at the generic point. Our method uses the Bloch–Levine moving technique and some properties of the Milnor K-theory norm for fields. Furthermore we give new applications.
Supported by Studienstiftung des deutschen Volkes and Deutsche Forschungsgemeinschaft. 相似文献
13.
Piotr Jaworski 《K-Theory》1996,10(1):83-105
Let V be a quasihomogeneous normal variety. The aim of this paper is to describe the Milnor K-theory of the function field of V in terms of the second residue homomorphisms associated with subvarieties and resolution data of V.Supported by KBN, 2 P301 010 06. 相似文献
14.
We investigate the Chow groups of zero cycles of products of curves over a p-adic field by means of the Milnor K-groups of their Jacobians as introduced by Somekawa. We prove some finiteness results for CH
0(X)/m for X a product of curves over a p-adic field. 相似文献
15.
Victor Bovdi 《Algebras and Representation Theory》2003,6(3):353-368
We give an explicit list of all p-groups G with a cyclic subgroup of index p
2, such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K-basis. We also prove that such a K-basis does not exist for the group algebra KG, in the case when G is either a non-Abelian powerful p-group or a two generated p-group (p2) with a central cyclic commutator subgroup. This paper is a continuation of the paper which appeared in Arch. Math. (Basel)
74 (2000), 217–285. 相似文献
16.
Bertin Diarra Fana Tangara 《P-Adic Numbers, Ultrametric Analysis, and Applications》2009,1(2):128-135
Let q be a principal unit of the ring of valuation of a complete valued field K, extension of the field of p-adic numbers. Generalizing Mahler basis, K. Conrad has constructed orthonormal basis, depending on q, of the space of continuous functions on the ring of p-adic integers with values in K. Attached to q there are two models of the quantum plane and a model of the quantum Weyl algebra, as algebras of bounded linear operators
on the space of p-adic continuous functions. For q not a root of unit, interesting orthonormal (orthogonal) families of these algebras are exhibited and providing p-adic completion of quantum plane and quantum Weyl algebras.
The text was submitted by the authors in English. 相似文献
17.
We show that for a field k of characteristic p, H
i
(k,ℤ(n)) is uniquely p-divisible for i≠n (we use higher Chow groups as our definition of motivic cohomology). This implies that the natural map K
n
M
(k)?K
n
(k) from Milnor K-theory to Quillen K-theory is an isomorphism up to uniquely p-divisible groups, and that K
n
M
(k) and K
n
(k) are p-torsion free. As a consequence, one can calculate the K-theory mod p of smooth varieties over perfect fields of characteristic p in terms of cohomology of logarithmic de Rham Witt sheaves, for example K
n
(X,ℤ/p
r
)=0 for n>dimX. Another consequence is Gersten’s conjecture with finite coefficients for smooth varieties over discrete valuation rings
with residue characteristic p. As the last consequence, Bloch’s cycle complexes localized at p satisfy all Beilinson-Lichtenbaum-Milne axioms for motivic complexes, except possibly the vanishing conjecture.
Oblatum 21-I-1998 & 26-VII-1999 / Published online: 18 October 1999 相似文献
18.
Bradley Weaver 《Israel Journal of Mathematics》2018,228(2):587-626
For a prime p, a cyclic-by-p group G and a G-extension L|K of complete discrete valuation fields of characteristic p with algebraically closed residue field, the local lifting problem asks whether the extension L|K lifts to characteristic zero. In this paper, we characterize D4-extensions of fields of characteristic two, determine the ramification breaks of (suitable) D4- extensions of complete discrete valuation fields of characteristic two, and solve the local lifting problem in the affirmative for every D4-extension of complete discrete valuation fields of characteristic two with algebraically closed residue field; that is, we show that D4 is a local Oort group for the prime 2. 相似文献
19.
O. Yu. Ivanova 《Journal of Mathematical Sciences》2007,147(5):7088-7097
A complete two-dimensional local field K of mixed characteristic with finite second residue field is considered. The existence
of a completely ramified extension L of K such that L is a standard field is assumed. It is proved that the rank of the quotient
U(1)K
2
top
K/TK, where TK is the closure of the torsion subgroup, is equal to the degree of the constant subfield of K over ℚp. I. B. Zhukov constructed a set of generators of this quotient in the case where K is a standard field. In this paper, two
natural generalizations of this set are considered, and it is proved that one of them generates the entire group and the other
generates its subgroup of finite index. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 343, 2007, pp. 206–221. 相似文献
20.
V. Bovdi 《Archiv der Mathematik》2000,74(2):81-88
Let K be a field of characteristic p and G a nonabelian metacyclic finite p-group. We give an explicit list of all metacyclic p-groups G, such that the group algebra KG over a field of characteristic p has a filtered multiplicative K-basis. We also present an example of a non-metacyclic 2-group G, such that the group algebra KG over any field of characteristic 2 has a filtered multiplicative K-basis. 相似文献