mathfrak p adic groups by f bruhat

Ngày tải lên: 13/11/2014, 10:06

... September 2009 The original and proper context of p- adic Lie groups is p- adic analysis This is the point of view in Part A Of course, in a formal sense the notion of a p- adic Lie group is completely ... Two Generators 175 25 The Operator P 178 26 Finite Rank Pro -p- Groups 181 27 Compact p- Adic Lie Groups 192 VI 195 Completed Group Rings of p- Valued Groups 28 The Ring Filtration 195 29 Analyticity ... Then, for any f ∈ F (K ˜ ˜ f ◦ g exists but the composite of power series f ◦ g ∈ F (K r ; V ) may not Exercise An example of such a situation is ∞ g(X) := X p − X ∈ F1 (Qp ; Qp ) and Y n ∈ F p...

Ngày tải lên: 29/06/2014, 09:20

Ngày tải lên: 13/11/2014, 11:05

... = f1 , f , , f n f1 f n f1 f f n f1 , f , , f n j= 21 f , , f n Wronskian hàm f , f , , f n f1 f f n W ( f ) = f1 , , f n = f '1 f '2 f 'n f1 (n 2) f 2(n 2) f n(n1 2) Do f , f , , f ... hàm f , , f n f1 f2 fn W ( f ) = f1 , ., fn = f '1 f '2 f 'n f1 (n )2 f2 (n )2 fn(n1 )2 Do f , f , , f n độc l p tuyến tính nên f , f , , f n f1 , , f n 13 Đặt P (t ) f , f , , f n ... fn f1 (n 1) f1 fn(n 1) fn Li ( f1 , ., f n ) = 1 f n f1 f1 fn f1 (n 1) Khi f1 f n(n 1) fn 12 L( f ) = Ư W ( f ) tơng tự Nếu Li ( f ) độc l p tuyến tính f1 , f , , f n L( f ) f1 f n ƯW( f...

Ngày tải lên: 18/12/2013, 20:03

... Z p a (mod p) nờn f( a ) cho f( a ) p (mod p f( a ) (mod p) Do ú tn ti ), (chng hn, l ch s ng vi lu tha p khai trin p- adic ca f( a )) Khi ú: f( a ) ( mod p ) p + f ' ( a0 ) b1 p + f ' ... ord p (x + y) = ord p (ad + bc) - ord p b - ord p d min(ord p ad, ord p bc) - ord p b - ord p d = min(ord p a + ord p d, ord p b + ord p c) - ord p b - ord p d = min(ord p a ord p b, ord p c ... mod p n ) vỡ Nu a b ( mod p n ) thỡ: b a = a b p p p n , Nu a b ( mod p n ) v b c ( mod p n ) thỡ: a a p = p n ú: b a ( mod p n ) a b p p n ( a c p = a b + b c p max a b p , b c p...

Ngày tải lên: 19/12/2013, 11:33

... có: p( + ) = p- k, k m p- m = max (p- n, p- m) với n m = max( p( ), p( )) Suy p( + ) max( p( ), p( )) a *) p( ) = p( b pn c m ac n +m p ) = p ( p ) = p ( n +m ) = p n p m = p ( ... i)Dãy + p+ + p2 + +pn+ ; trờng p- adic RP dãy hội tụ, (pn) = pn (nghĩa số hạng tổng quát tiến đến 0) Ta có Sn = + p+ + p + +p + = Do đó, tổng cho n 1p p n +1 + p p -17- , suy lim Sn = p ii)Trong ... f( c) (mod p) f( c) (mod p) tồn số nguyên p- adic cho: f( ) = 0, c (mod p) Chứng minh Bằng phơng ph p qui n p theo n, ta dựng dãy số nguyên padic { x n } cho xn c (mod p) , xn xn-1 (mod pn-1),...

Ngày tải lên: 22/12/2013, 13:12

... Ta có: x p = am a b = p a b p mb p mb p = np i 10 p =n p / p i / p i mb Mặt khác từ định lý ph p chia có d ta có: = kpi + r, r < pi Khi r x = kp i x p max{ x , kp i p p p } pi Vậy số ... p i i i p i p p i i p i p p p i j N( j) p j+ j+ i N ( j+) i p i j N ( j +) p j j j+ p N ( j) N ( j) N ( j+ ) j p i N ( j+ ) N ( j) N ( j) N ( j) j N ( j) j N ( j) p p i p i i j p p i N ( j) p ... a0 + a 1p + a 2p2 +, < p Zp vành Qp không ớc 11 Đặt Z* p {x Zp x x = {x Zp: p =1} Z* p / zp} {x Zpx (modp)} nhóm nhân phần tử khả nghịch Các phần tử Z* p gọi phần tử đơn vị vành Zp Mệnh đề...

Ngày tải lên: 23/12/2013, 17:05

... cho p, m, n Z, n m Ta có + = a n c m adp n m + bc m p + p = p b d bd Khi ta có p( +) = p- k , (k m) p- m = max (p- n ,p- m) với n m = max (p( ), p( )) 15 Suy p( +) max (p( ), p( )) +/ p( .) = p( a ... dãy + p + p2 ++pn + ; trờng p- adic Rp dãy hội tụ (pn) = pn ( nghĩa số hạng tổng quát tiến đến ) ta có Sn = + p + p2 + + pn + = Do tổng cho p n +1 + , p p suy limSn = 1p 1p ii/ Trong trờng adic ... p p ) b d ac = p ( bd p n +m ) = p- (n+m) = p- n .p- m = p( ) .p( ) Vậy p( .) = p( ) .p( ) Chuẩn p đợc xác định nh đợc gọi chuẩn p adic Q 1.8.2 Định nghĩa Mở rộng đầy đủ trờng số hữu tỷ Q theo chuẩn p...

Ngày tải lên: 23/12/2013, 19:12

... diễn viết: f = ( f0 , f2 , , fn) : P IPn( ) p ( f0 (z), f1 (z), , fn(z)) z 1.6.3 Định nghĩa Độ cao ánh xạ chỉnh hình p- adic f = (f0 , f1 , , fn) không gian xạ ảnh n chiều là: IPn( ) p h (f, t) = ... n1) W ( f ) = f1 , f , , f n f1 / p- adic ( f n1) ( f n n 1) = đợc gọi Wronskian hàm chỉnh hình p- adic f1 , f2 , , fn 1.11.2 Mệnh đề Nếu f1 , f2 , , fn độc l p tuyến tính thì: W (f) / 1.11.3 Mệnh ... a p đợc gọi không điểm hàm nguyên f hàm không, nghĩa a nghiệm phơng trình f( z) = 1.2.5 Định lý Picard p- adic (xem [1]) Nếu hàm nguyên p- adic f không điểm p f số 1.3 Hàm phân hình p- adic f (...

Ngày tải lên: 27/12/2013, 14:17

... see [1, p 152], if G [F] := KerFG = ImVG =: V(G) and G[V] = F( G) (in particular this implies that G is annihilated by p) Such group schemes over a perfect field appear as the p- kernel of a p- divisible ... direct summand of M This finishes the proof of (2), and ends the proof of the proposition 2(2.2) Split extensions and proof of the theorem In this section we prove a proposition on split extensions ... The slope λ = 1, given by the pair (0, 1), defines the p- divisible group G0,1 = Qp /Zp and its p- kernel is Z/pZ These p- divisible groups and their p- kernels split off naturally over a perfect field;...

Ngày tải lên: 16/02/2014, 05:20

... số phức p- adic, trường số phức p- adic C p , Chương 2: Xây dựng chuỗi Laurent p- adic : Trình bày thêm số khái niệm: Chuỗi Laurent p- adic, vành chuỗi Laurent p- adic, chuẩn chuỗi Laurent p- adic, ... K (f, s) = K (f, r) mà K (f, r) ≤ k (f, s) ≤ K (f, s) (do s ≥ r) nên: K (f, r) = k (f, s) = K (f, s) (2.38) và: ∀s ∈ (r − ξ, r], k (f, s) = k (f, r) mà k (f, r) ≥ K (f, s) ≥ k (f, s) (do s ≤ r) nên: k (f, ... (Qp , | |) : Ta có: Nhóm giá trò (Q p , | |) là: |Q∗ | = {|x| : x ∈ Q∗ } = {pm : m ∈ Z} p p Đặt: Zp = {x ∈ Qp : |x| ≤ 1} Và: M = {x ∈ Qp : |x| < 1} = pZp Trường thặng dư (Q p , | |) là: Qp = Zp...

Ngày tải lên: 19/02/2014, 08:30

... Naval Forces of the Empire, actually in being a land army of five divisions and two mounted divisions, fully officered, fully equipped, and stamped with the seal of brilliantly successful performance; ... quartered in different places They were as indifferent as they were different, but any place which afforded shelter from the rain and protection from the cold was greatly appreciated Despite the inconveniences ... inscribed by his O.C He was a fine fellow, full of fun and life, a true comrade, an ideal officer, beloved by all who knew him The following pathetic incident speaks of the attachment which springs up...

Ngày tải lên: 06/03/2014, 03:21

... admits of only one answer The fox eats the pheasant; the pheasant is eaten by the fox This not very complex proposition may read like an excerpt from a French grammar, but it is the epitome of the ... destructive larva of the crane-fly, in which case it may more than pay its footing in the fields The foodstuff most fatal to itself is the yew leaf, for which, often with fatal results, it seems ... many an escape to this habit of hissing, accompanied by a vigorous twisting of its neck and the infliction of a sufficient peck, easily mistaken in a moment of panic for the bite of an angry adder...

Ngày tải lên: 06/03/2014, 13:20

... Der p ELISA and competitive RIA were compared by parallelline analyses RESULTS Sequence analyses of mature and pro-Der p cDNAs of mature and pro-Der p were picked up by PCR from a kgt11 D pteronyssinus ... yield of 55 mgáL)1 (competitive RIA) [29] Af®nity puri®cation of rpro-Der p gave a ®nal puri®cation yield of 15% nDer p 1, rpro-Der p and Endo H-treated rproDer p were separated by SDS/PAGE (4±12% ... which were performed for rDer f [20] (buffer exchange to pH 4.0) and rpro-Der p [18] [buffer exchange to pH 4.0, addition of cysteine, and heating to 60 °C (with/ Fig Der p ELISA rpro-Der p was times...

Ngày tải lên: 17/03/2014, 11:20

... extension of C(k), let π be a uniformizer of O, and fix once and for all a ring endomorphism σ0 on O lifting the absolute Frobenius f x → xp on k Let q = pf be a power of p and put σ = σ0 (In principle, ... Therefore the endpoints of the segment of the Newton polygon of x of slope −s are (v0 (ui ), vp (π i )) and (v0 (uj ), vp (π j )) Thus the multiplicity of s as a slope of x is vp (π j ) − vp (π ... implies that N has rank n − r and F/ N is free of rank r Now localizing at each prime p of R, we obtain a surjection Mp → (F/ N )p of free modules of the same rank By a standard result, this map...

Ngày tải lên: 22/03/2014, 16:20

... Example 2.15 Use the same norm as in Example 2.14 with an = (1 + p) p − Then for n = 1, |an |p = |(1 + p) p − 1 |p p p p + ··· + pp−1 + pp p 1 = p = 2, p since for k p − 1, ordp p k = Hence |a1 |p ... p α0 ≡ α0 , p hence p |α0 − α0 |p < But this gives p p | p − α |p = |( p − α0 ) + (α0 − α0 ) + (α0 − α) |p p p max{| p − α0 |p , |α0 − α0 |p , |α0 − α |p } since p p−1 | p − α0 |p = (α − α0 )( p 1 ... is true for n = by the above Suppose true for n Then n+1 p n = p + β say, where |β |p < 1/pn Raising to the power p gives n+2 p n = ( p + β )p n+1 = p n (p 1) + p p β + ··· + p pn k p k α β...

Ngày tải lên: 31/03/2014, 15:19

Ngày tải lên: 24/04/2014, 17:15

... OQp = Qp [0; 1] = Qp (0; p) t p vừa đóng, vừa mở, gọi vành số nguyên p adic kí hiệu Zp Với n ∈ Z+ , vành Zp phủ t p Qp [k; p n ] = k + pn Zp , k = 0, 1, , pn − Điều kéo theo Zp compact, Qp ... = pvp (x) x ; y = pvp (y) y với x , y có tử mẫu không chia hết cho p Ta thấy x.y = pvp (x)+vp (y) x y hiển nhiên x y có tử mẫu không chia hết cho p Suy |x.y |p = p (vp (x)+vp (y)) = p vp (x) p vp ... hiển nhiên, f (Cp [0; r]) ⊂ Cp [f (0); s] Mặt khác với b ∈ Cp [f (0); s], xét hàm số g(z) = f (z) − b Nếu s = 0, f − f (0) = 0, suy f = f (0) hàm Do f (Cp [0; r]) = Cp [f (0), 0] = {f (0)}, Định...

Ngày tải lên: 31/05/2014, 08:48

... about replacing β α by βn,q Let fn x definition 1.2 of p- adic q-integral on p, we easily get qIq f1 pN N→∞ lim N →∞ pN f x n By the pN −1 q lim 1.5 if n > 1, f x qx , q x pN −1 N f x qx q x f x ... of Inequalities and Applications Let UD p be the space of uniformly differentiable functions on p For f ∈ UD the p- adic q-integral on p, which is called the bosonic q-integral on p, is defined by ... x lim f pN qp − f pN N →∞ 1.6 q q−1 f , log q q−1 f p Continuing this process, we obtain easily the relation fn x dμq x − qn p where n ∈ Æ and f l f x dμq x p df l /dx see q−1 n−1 l ql f l q...

Ngày tải lên: 21/06/2014, 06:20

... Journal of Inequalities and Applications Let UD Zp be the space of uniformly differentiable function on Zp For f ∈ UD Zp , the p- adic invariant q-integral on Zp is defined as Iq f Zp f x dμq x ... Journal of Inequalities and Applications Now we construct the twisted p- adic q-integral on Zp as follows: Iq,ζ f Zp f x dμq,ζ x pN −1 lim N →∞ f x μq,ζ x pN Zp 2.3 x pN −1 lim f x qx ζx , pN N →∞ ... polynomials by using the properties of the p- adic invariant q-integral on Zp cf In this paper, we define the twisted p- adic q-integral on Zp and extend our result to the twisted q-Bernoulli polynomials...

Ngày tải lên: 21/06/2014, 07:20