Đề tài "Iwasawa’s Main Conjecture for elliptic curves over anticyclotomic Zp-extensions" pot

... Mathematics Iwasawa’s Main Conjecture for elliptic curves over anticyclotomic Zp-extensions By M. Bertolini and H. Darmon IWASAWA’S MAIN CONJECTURE FOR ELLIPTIC CURVES 19 Lemma 2.7. ... #S over Λ/p n Λ. IWASAWA’S MAIN CONJECTURE FOR ELLIPTIC CURVES 23 Proof. The fact that H 1 S (K m ,T f,n ) is free over Z/p n Z[G m ] is essentially Theore...

Ngày tải lên: 06/03/2014, 08:21

... H 0 (y)=P for all y in a neighborhood of x. Consequently, H  (y)=P in a neighborhood of x, for all  ≥ 1, proving (3). For the induction step, fix k ≥ 0, and assume the lemma holds for that k. We ... H 2k+2 (y) < dim H 2k+1 (y) for y arbitrarily near x.(9) Then, since we are assuming Lemma 2.2 for k, we must have dim H 2k+1 (y) < dim P−k for all y as in (9), and therefore...

Ngày tải lên: 15/03/2014, 09:20

... inside  Sp 2m (k). Let Z l be the standard maximal unipotent subgroup of GL l (k). Then, since the covering of  Sp 2m (k) splits over unipotent subgroups ([Mt]), U n = m(Z n ) · V n ,  U m =  m(Z m )N m × ... bilinear form satisfying (2.9) b ψ U (ω ψ (u, h)ϕ, π ∨ m (h)ξ)=ψ U (u)b ψ U (ϕ, ξ) for u ∈ U n , h ∈  Sp 2m (k), ϕ ∈S(V m ), ξ ∈ V π ∨ m .Wewill show that, for m<n, the spa...

Ngày tải lên: 22/03/2014, 15:21

... (for i =1, 2, 3) and A −1 1 A 4 A 1 A −2 4 = U 4 (x L )U 4 (x R ), and [x L j ,x R k ] = 1 for all j,k ∈{1, 2, 3}, and A ε i x L j A −ε i = V ijε (x L ) and A ε i x R j A −ε i = V ijε (x R ) for ... a normal subgroup. To obtain a finite generating set for P , one chooses a finite normal generating set for N 1 and then appends a generating set for ∆ ∼ = H. The question of when P is fin...

Ngày tải lên: 28/03/2014, 22:20

... The main conjecture for CM elliptic curves at supersingular primes By Robert Pollack and Karl Rubin Annals of Mathematics, 159 (2004), 447–464 The main conjecture for CM elliptic curves ... the main conjecture for CM elliptic curves at ordinary primes. We sketch the ideas briefly here, but we defer the precise definitions, statements, and references to...

Ngày tải lên: 28/03/2014, 22:20

... ) fr (1) (and similarly for the l-adic and de Rham realizations). This conjecture has been proved for curves [10], for the second cohomology of projective surfaces [9], and for the first cohomology ... implies the original conjecture up to isogeny. If the degree of cohomology is at most two,wecan prove the conjecture for the Hodge realization without isogeny, and even for 1...

Ngày tải lên: 14/02/2014, 17:20

... symmetric modular forms over Z[1/2] is generated by forms φ 2 ,χ 6 , and χ 10 of weights 2, 6, and 10. The form φ 2 is the weight 2 Eisenstein series, while χ 6 and χ 10 are cuspforms. It follows ... modular form f over O E is integral over the ring of symmetric even-weight modular forms studied by Nagaoka. In particular, since φ 2 ,χ 6 , and χ 10 generate this ring, we have that f(A, η...

Ngày tải lên: 16/02/2014, 05:20

... forms in general. In this paper we will address the question of existence of cusp forms for the group G =SL n . The main purpose of this paper is to prove that cusp forms exist in abundance for ... cusp forms for Γ. By Langlands’ theory of Eisenstein series [La], cusp forms are the build- ing blocks of the spectral resolution of the regular representation of G(R)in L 2 (Γ\G(R)). Cusp...

Ngày tải lên: 29/03/2014, 07:20

... mouse_click(); delay(1000); setcolor(15); for( int x=0;x<=n;x++) line(startx, starty+x*width/n, startx+width, starty+x*width/n); //ke duong ngang for( int y=0;y<=n;y++) line(startx+y*width/n, ... line(startx+y*width/n, starty, startx+y*width/n, starty+width); //ke duong doc for( int x=1;x<=n;x++) for( int y=1;y<=n;y++) if((x+y)%2) floodfill(startx+x*width/n...

Ngày tải lên: 23/12/2013, 12:47

... slow dimension growth condition for AH algebras (and therefore, a fortiori for ASH algebras), one obtains counterexamples to the Elliott conjecture of a particularly forceful nature, so that slow ... Rørdam both for suggesting the search for the automorphisms of Theorem 1.2 and for several helpful discussions, Søren Eilers and Copenhagen University for their hospitality in 2003,...

Ngày tải lên: 16/02/2014, 06:20