Annales Mathematiques du Quebec最新文献

Let L/F be a finite Galois extension of number fields with an arbitrary Galois group G. We give an explicit description of the kernel of the natural map on motivic cohomology of the rings of integers (H^2_mathcal {M}(o_L, {textbf{Z}}(i))_{G} {longrightarrow } H^2_mathcal {M}(o_F, {textbf{Z}}(i))). Using the link between motivic cohomology and K-theory, we deduce genus formulae for all even K-groups (K_{2i-2}(o_F)) of the ring of integers. As a by-product, we answer a question raised by B. Kahn about a signature map.

For certain elliptic differential operators L,  we study the behaviour of solutions to (Lu=0,) as we tend to the boundary along radii in strictly starlike domains in (mathbb {R}^n, nge 3.) Analogous results are obtained in other special domains. Our approach involves introducing harmonic line bundles as instances of Brelot harmonic spaces and approximating continuous functions by harmonic functions on appropriate subsets. We are required to approximate on certain closed sets, which is not obvious, since the space of continuous functions on an (unbounded) closed set, endowed with the topology of uniform convergence, is not a topological vector space, though it is both a vector space and a topological space.

Let K be an imaginary quadratic field where a prime number (p ge 5) is inert. Let E be an elliptic curve defined over K and suppose that E has good supersingular reduction at p. In this paper, we prove that the plus/minus Selmer group of E over the anticyclotomic ({{,mathrm{mathbb {Z}},}}_{p})-extension of K has no proper (Lambda )-submodules of finite index under mild assumptions for E. This is an analogous result to R. Greenberg and B. D. Kim for the anticyclotomic ({{,mathrm{mathbb {Z}},}}_{p})-extension essentially. By applying the results of A. Agboola–B. Howard or A. Burungale–K. Büyükboduk–A. Lei, we can also construct examples satisfying the assumptions of our theorem.

We present a new and simpler proof of the fact that any Lagrangian ({mathbb {R}}P^2) in (T^*{mathbb {R}}P^2) is Hamiltonian isotopic to the zero section. Our proof mirrors the one given by Li and Wu for the Hamiltonian uniqueness of Lagrangians in (T^*S^2), using surgery to turn Lagrangian spheres into symplectic ones. The main novel contribution is a detailed proof of the folklore fact that the complement of a symplectic quadric in ({mathbb {C}}P^2) can be identified with the unit cotangent disc bundle of ({mathbb {R}}P^2).

In this paper, we describe the classification of all the geometric fibrations of a closed flat Riemannian 4-manifold over a connected 1-orbifold.

The purpose of this note is to find explicit representatives in de Rham cohomology for the generators of the cohomology of the moduli space of parabolic bundles, analogous to the results of [5] for the moduli space of vector bundles. Further we use the explicit generators to compute the intersection pairing of its cohomology.

We investigate elliptic operators with a symmetry that forces their index to vanish. We study the secondary index, defined modulo 2. We examine Callias-type operators with this symmetry on non-compact manifolds and establish mod 2 versions of the Gromov–Lawson relative index theorem, the Callias index theorem, and the Boutet de Monvel’s index theorem for Toeplitz operators.

Let E be an elliptic curve over (mathbb {Q}). Greenberg has posed a question whether the structure of the fine Selmer group over the cyclotomic (mathbb {Z}_{p})-extension of (mathbb {Q}) can be described by cyclotomic polynomials in a certain precise manner. A recent work of Lei has made progress on this problem by proving that the fine Mordell–Weil group (in the sense of Wuthrich) does have this required property. The goal of this paper is to study analogous questions of Greenberg over various (mathbb {Z}_{p})-extensions of an imaginary quadratic field F. In particular, when the elliptic curve has complex multiplication by the ring of integers of the imaginary quadratic field, we obtain results that are analogous to those of Lei over the cyclotomic (mathbb {Z}_{p})-extension and anti-cyclotomic (mathbb {Z}_{p})-extension of F. In the event that the elliptic curve has good ordinary reduction at the prime p, we further obtain a result over the (mathbb {Z}_{p})-extension of F unramified outside precisely one of the prime of F above p. Finally, we study the situation of an elliptic curve over the anticyclotomic (mathbb {Z}_{p})-extension under the generalized Heegner hypothesis. Along the way, we establish an analogous result for the BDP-Selmer group. This latter result is then applied to obtain a relation between the BDP p-adic L-function and the Mordell–Weil rank growth in the anticyclotomic (mathbb {Z}_{p})-extension which may be of independent interest.