共查询到20条相似文献,搜索用时 390 毫秒
1.
Shreeram S. Abhyankar 《Israel Journal of Mathematics》1994,86(1-3):1-23
There are various natural local zeta functions associated with groups and rings for each primep. We consider the question of how these functions behave as we vary the primep and the groups (or rings) range over a specific class of groups (or rings), e.g. finitely generated torsion-free nilpotent
groups of a fixed Hirsch length orp-adic analytic groups of a fixed dimension. Using a result of Macintyre’s on the uniformity of parameterizedp-adic integrals, together with various natural parameter spaces we define for these classes of groups, we prove a strong finiteness
theorem on the possible poles of these local zeta functions. 相似文献
2.
The notions Hodge–Newton decomposition and Hodge–Newton filtration for F-crystals are due to Katz and generalize Messing’s result on the existence of the local-étale filtration for p-divisible groups. Recently, some of Katz’s classical results have been generalized by Kottwitz to the context of F-crystals with additional structures and by Moonen to μ-ordinary p-divisible groups. In this paper, we discuss further generalizations to the situation of crystals in characteristic p and of p-divisible groups with additional structure by endomorphisms. 相似文献
3.
Kazuya Kato 《K-Theory》2005,34(2):99-140
We compute K1 of completed group rings of some two dimensional p-adic Lie groups.
Dedicated to Professor Spencer Bloch on his sixtieth birthday 相似文献
4.
We first study the growth properties of p-adic Lie groups and its connection with p-adic Lie groups of type R and prove that a non-type R p-adic Lie group has compact neighbourhoods of identity having exponential growth. This is applied to prove the growth dichotomy
for a large class of p-adic Lie groups which includes p-adic algebraic groups. We next study p-adic Lie groups that admit recurrent random walks and prove the natural growth conjecture connecting growth and the existence
of recurrent random walks, precisely we show that a p-adic Lie group admits a recurrent random walk if and only if it has polynomial growth of degree at most two. We prove this
conjecture for some other classes of groups also. We also prove the Choquet-Deny Theorem for compactly generated p-adic Lie groups of polynomial growth and also show that polynomial growth is necessary and sufficient for the validity of
the Choquet-Deny for all spread-out probabilities on Zariski-connected p-adic algebraic groups. Counter example is also given to show that certain assumptions made in the main results can not be
relaxed. 相似文献
5.
Andrei Yu. Khrennikov Jan Harm Van der Walt 《P-Adic Numbers, Ultrametric Analysis, and Applications》2011,3(4):326-333
The usage of the fields of p-adic numbers Q
p
, rings of m-adic numbers Q
m
and more general ultrametric rings in theoretical physics induced the interest to topological-algebraic studies on topological
extensions of rational and real numbers and more generally (commutative and even noncommutative) rings. It is especially interesting
to investigate a possibility to proceed to non-Archimedean rings by starting with real numbers. In particular, in this note
we present “no-go” theorems (Theorems 3, 4) by which one cannot obtain an ultrametric ring by extending (in a natural way)
the ring of real numbers. This puremathematical result has some interest for non-Archimedean physics: to explore ultrametricity
one has to give up with the real numbers — to work with rings of e.g. m-adic numbers (where m > 1 is a natural, may be nonprime, number). 相似文献
6.
Sergio Albeverio Sergei V. Kozyrev 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(4):265-277
The approach to p-adic wavelet theory from the point of view of representation theory is discussed. p-Adic wavelet frames can be constructed as orbits of some p-adic groups of transformations. These groups are automorphisms of the tree of balls in the p-adic space. In the present paper we consider deformations of the standard p-adic metric in many dimensions and construct some corresponding groups of transformations. We build several examples of p-adic wavelet bases. We show that the constructed wavelets are eigenvectors of some pseudodifferential operators. 相似文献
7.
R.R. Andruszkiewicz 《Quaestiones Mathematicae》2018,41(4):483-491
The first example of a finite rank torsion-free abelian group A such that the quotient group of A modulo the square subgroup of A is not a nil-group is indicated (in both cases of associative and general rings). In particular, the answer to the question posed by A.E. Stratton and M.C. Webb in [18], Abelian groups, nil modulo a subgroup, need not have nil quotient group, Publ. Math. Debrecen. 27 (1980), 127–130, is given for finite rank torsion-free groups. A relationship between nontrivial p-pure subgroups of the additive group of p-adic integers and nontrivial ? [p?1]-submodules of the field of p-adic numbers is investigated. In particular, a bijective correspondence between these structures is proven using only elementary methods. 相似文献
8.
Gabriele Nebe 《Journal of Algebra》1998,210(2):189
This paper describes the ring-theoretic structure of the group rings ofSL2(p2) over thep-adic integers. 相似文献
9.
In this paper we consider the associativity of a (3, 2k + 1)-associative ring R in the following cases: (1) R is simple 2-divisible; (2) R is p-divisible trivial right ideal ring; (3) R is prime p-divisible.AMS Subject Classification: 17A30 相似文献
10.
本文研究了p-可除kG-模,这是一类由群阶的素数因子来控制的模类.利用Heller算子,证明了n次Heller算子置换非投射不可分解p-可除kG-模的同类;利用模的诱导和限制方法,证明了若H是G的强p-嵌入子群,则Green对应建立了不可分解p-可除kG-模的同构类与不可分解p-可除kH-模的同构类之间的一一对应.推广了不可分解相对投射kG-模上的Green对应. 相似文献
11.
Marco A. Garuti 《Mathematische Annalen》2008,341(3):603-622
On a scheme S over a base scheme B we study the category of locally constant BT groups, i.e. groups over S that are twists, in the flat topology, of BT groups defined over B. These groups generalize p-adic local systems and can be interpreted as integral p-adic representations of the fundamental group scheme of S/B (classifying finite flat torsors on the base scheme) when such a group exists. We generalize to these coefficients the Katz
correspondence for p-adic local systems and show that they are closely related to the maximal nilpotent quotient of the fundamental group scheme. 相似文献
12.
Our main aim in this paper is to give a foundation of the theory of p-adic multiple zeta values. We introduce (one variable) p-adic multiple polylogarithms by Colemans p-adic iterated integration theory. We define p-adic multiple zeta values to be special values of p-adic multiple polylogarithms. We consider the (formal) p-adic KZ equation and introduce the p-adic Drinfeld associator by using certain two fundamental solutions of the p-adic KZ equation. We show that our p-adic multiple polylogarithms appear as coefficients of a certain fundamental solution of the p-adic KZ equation and our p-adic multiple zeta values appear as coefficients of the p-adic Drinfeld associator. We show various properties of p-adic multiple zeta values, which are sometimes analogous to the complex case and are sometimes peculiar to the p-adic case, via the p-adic KZ equation. 相似文献
13.
Saharon Shelah 《Israel Journal of Mathematics》1984,49(1-3):239-257
Two lines of research are involved here. One is a combinatorial principle, proved in ZFC for many cardinals (e.g., any λ =
λℵ
0) enabling us to prove things which have been proven using the diamond or for strong limit cardinals of uncountable cofinality.
The other direction is building abelian groups with few endomorphisms and/or prescribed rings of endomorphisms. We prove that
for a ringR, whose additive group is thep-adic completion of a freep-adic module,R is isomorphic to the endomorphism ring of some separable abelianp-groupG divided by the ideal of small endomorphisms, withG of power λ for any λ = λℵ
0≧|R|.
Dedicated to the memory of Abraham Robinson on the tenth anniversary of his death
The author would like to thank the United States-Israel Binational Science Foundation for partially supporting this research. 相似文献
14.
V. S. Varadarajan Jukka T. Virtanen 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(2):157-174
It is well known that at distances shorter than Planck length, no length measurements are possible. The Volovich hypothesis
asserts that at sub-Planckian distances and times, spacetime itself has a non-Archimedean geometry. We discuss the structure
of elementary particles, their classification, and their conformal symmetry under this hypothesis. Specifically, we investigate
the projective representations of the p-adic Poincaré and Galilean groups, using a new variant of the Mackey machine for projective unitary representations of semidirect
products of locally compact and second countable (lcsc) groups. We construct the conformal spacetime over p-adic fields and discuss the imbedding of the p-adic Poincaré group into the p-adic conformal group. Finally, we show that the massive and the so called eventually masssive particles of the Poincaré group
do not have conformal symmetry. The whole picture bears a close resemblance to what happens over the field of real numbers,
but with some significant variations. 相似文献
15.
Encoding the hierarchical structure of images by p-adic numbers allows for image processing and computer vision methods motivated from arithmetic physics. The p-adic Polyakov action leads to the p-adic diffusion equation in low level vision. Hierarchical segmentation provides another way of p-adic encoding. Then a topology on that finite set of p-adic numbers yields a hierarchy of topological models underlying the image. In the case of chain complexes, the chain maps
yield conditions for the existence of a hierarchy, and these can be expressed in terms of p-adic integrals. Such a chain complex hierarchy is a special case of a persistence complex from computational topology, where
it is used for computing persistence barcodes for shapes. The approach is motivated by the observation that using p-adic numbers often leads to more efficient algorithms than their real or complex counterparts. 相似文献
16.
V. Anashin 《P-Adic Numbers, Ultrametric Analysis, and Applications》2012,4(2):151-160
In the paper we develop the p-adic theory of discrete automata. Every automaton
\mathfrakA\mathfrak{A} (transducer) whose input/output alphabets consist of p symbols can be associated to a continuous (in fact, 1-Lipschitz) map from p-adic integers to p-adic integers, the automaton function
f\mathfrakA f_\mathfrak{A} . The p-adic theory (in particular, the p-adic ergodic theory) turned out to be very efficient in a study of properties of automata expressed via properties of automata
functions. In the paper we prove a criterion for finiteness of the number of states of automaton in terms of van der Put series
of the automaton function. The criterion displays connections between p-adic analysis and the theory of automata sequences. 相似文献
17.
In this paper p-adic analogs of the Lichtenbaum Conjectures are proven for abelian number fields F and odd prime numbers p, which generalize Leopoldt's p-adic class number formula, and express special values of p-adic L-functions in terms of orders of K-groups and higher p-adic regulators. The approach uses syntomic regulator maps, which are the p-adic equivalent of the Beilinson regulator maps. They can be compared with étale regulators via the Fontaine-Messing map,
and computations of Bloch-Kato in the case that p is unramified in F lead to results about generalized Coates-Wiles homomorphisms and cyclotomic characters.
Oblatum 14-V-96 & 9-X-97 相似文献
18.
Zoran Šunić 《Geometriae Dedicata》2007,124(1):213-236
For every prime p and every monic polynomial f, invertible over p, we define a group G
p, f
of p-adic automorphisms of the p-ary rooted tree. The groups are modeled after the first Grigorchuk group, which in this setting is the group . We show that the constructed groups are self-similar, regular branch groups. This enables us to calculate the Hausdorff
dimension of their closures, providing concrete examples (not using random methods) of topologically finitely generated closed
subgroups of the group of p-adic automorphisms with Hausdorff dimension arbitrarily close to 1. We provide a characterization of finitely constrained
groups in terms of the branching property, and as a corollary conclude that all defined groups are finitely constrained. In
addition, we show that all infinite, finitely constrained groups of p-adic automorphisms have positive and rational Hausdorff dimension and we provide a general formula for Hausdorff dimension
of finitely constrained groups. Further “finiteness” properties are also discussed (amenability, torsion and intermediate
growth).
Partially supported by NSF grant DMS-0600975. 相似文献
19.
Stavros Tsalidis 《K-Theory》2000,21(2):151-199
We investigate étale descent properties of topological Hochschild and cyclic homology. Using these properties we deduce a general injectivity result for the descent map in algebraic K-theory, and show that algebraic K-theory has étale descent for rings of integers in unramified and tamely ramified p-adic fields. 相似文献
20.
Kenji Kamizono 《Proceedings of the Steklov Institute of Mathematics》2009,265(1):115-130
In this paper, we generalize the result of Bikulov and Volovich (1997) and construct a p-adic Brownian motion over ℚ
p
. First, we construct directly a p-adic white noise over ℚ
p
by using a specific complete orthonormal system of (ℚ
p
). A p-adic Brownian motion over ℚ
p
is then constructed by the Paley-Wiener method. Finally, we introduce a p-adic random walk and prove a theorem on the approximation of a p-adic Brownian motion by a p-adic random walk. 相似文献