Tài liệu Đề tài " Serre’s conjecture over F9 " doc

... Mathematics Serre’s conjecture over F9 By Jordan S. Ellenberg SERRE’S CONJECTURE OVER F 9 1129 The intersection L ∩S ¯ρ is a zero-dimensional scheme of degree 4 over K  . Modifying ... O-module schemes over E. It follows that A i has semistable re- duction over O E , since no nontrivial finite-order element of GL 2 (Z 3 ( √ 5)) is congruent to 1 mod 3. SERRE’...

Ngày tải lên: 16/02/2014, 05:20

... similarly the additive category V X consisting of proper k-varieties over X, where the morphisms are assumed to be defined over X in the above definition. Since these are additive categories, we ... quasi- projective resolution over XD,ifX  • ∈C b XD nsqp and u is a strong quasi- isomorphism in K b X .Wesay that u is a quasi-projective resolution of degree ≥ j over XD,iffurthermo...

Ngày tải lên: 14/02/2014, 17:20

... Tr[γ]=N  = inf {E HF (γ):0≤ γ ≤ I, Tr[γ]=N } and if the infimum over all density matrices (the inf on the right) is attained then so is the infimum over projections (the inf on the left). We now come to ... 7))A  |x| −ζ . Annals of Mathematics The ionization conjecture in Hartree-Fock theory By Jan Philip Solovej* THE IONIZATION CONJECTURE IN HARTREE-FOCK THEORY 527 We...

Ngày tải lên: 14/02/2014, 16:20

... argument proves Theorem 3.7 over an arbitrary field k [Gab01, Proposition 2.4]. BERTINI THEOREMS OVER FINITE FIELDS 1113 (2) It is also true that any abelian variety over a field k can be embedded ... 1, since a scheme of finite type over F q can be viewed as a scheme of finite type over Z. On the other hand, ζ Spec Z (s) is the Riemann zeta function. The abc conjecture, formulated by...

Ngày tải lên: 14/02/2014, 17:20

... projective variety of dimension n over C, with a very ample line bundle O X (1), and let G be a connected algebraic reductive group. A principal GL(R, C)-bundle over X is equivalent to a vector ... S, is a pair  E S ,ϕ S : E S ⊗ E S −→ det E ∨∨ S  where E S is a coherent sheaf on X × S, flat over S, such that for every point s of S, E S ⊗ k(s) is torsion free, and the homomorphism ϕ S...

Ngày tải lên: 16/02/2014, 05:20

... P ¨ AIV ¨ ARINTA 3. Beltrami operators The Beltrami differential equation (1.4) and its solutions are effectively governed and controlled by two basic linear operators, the Cauchy transform and the Beurling transform. ... of the transform (5.16) below, we see in particular that S( ∂ϕ)=∂ϕ for ϕ ∈ C ∞ 0 (C).(3.4) Moreover, we have S = R 2 1 +2iR 1 R 2 − R 2 2 , CALDER ´ ON’S INVERSE CONDUCTIVITY...

Ngày tải lên: 16/02/2014, 05:20

... in Γ and Γ  WF R w = ∅. Moreover, χ(τ,η) ∈ S 0 1,0 (R n+1 )is equal to 1 in Γ, |τ |≤C|η| in supp χ(τ,η), and F w ∈ C ∞ (R, Ψ 1 1,0 (R n )) has THE NIRENBERG-TREVES CONJECTURE 415 real principal ... S(MH 1/2 1 ,G 1 ). Annals of Mathematics The resolution of the Nirenberg-Treves conjecture By Nils Dencker THE NIRENBERG-TREVES CONJECTURE 423 The denominator D = |f  | + h...

Ngày tải lên: 16/02/2014, 05:20

... let E n = {x : ν x (K n ) > 1/n}. DYNAMICS OF SL 2 ( R ) OVER MODULI SPACE IN GENUS TWO 407 Clearly E n is U-invariant and  E n = G/Γ. Moreover, if we take f ∈ C 0 (X) with f ≥ 0 and f =1onE n , ... group. Let ΩT g →T g denote the bundle whose fiber over X is Ω(X) −{0}. The space ΩT g is the complement of the zero-section of a holomorphic line bundle over T g . The mapping class grou...

Ngày tải lên: 16/02/2014, 06:20