We show that if a diffeomorphism of a symplectic manifold ((M^{2n},omega )) preserves the form (omega ^{k}) for (0< k < n) and is connected to identity through such diffeomorphisms then it is indeed a symplectomorphism.
We show that if a diffeomorphism of a symplectic manifold ((M^{2n},omega )) preserves the form (omega ^{k}) for (0< k < n) and is connected to identity through such diffeomorphisms then it is indeed a symplectomorphism.
For a given Coleman family of modular forms, we construct a formal model and prove the existence of a family of Galois representations associated to the Coleman family. As an application, we study the variations of Iwasawa (lambda )- and (mu )-invariants of dual fine (strict) Selmer groups over the cyclotomic (mathbb {Z}_p)-extension of (mathbb {Q}) in Coleman families of modular forms. This generalizes an earlier work of Jha and Sujatha for Hida families.
We give a new description of the logarithm matrix of a modular form in terms of distributions, generalizing the work of Dion and Lei for the case (a_p=0). What allows us to include the case (a_pne 0) is a new definition, that of a distribution matrix, and the characterization of this matrix by p-adic digits. One can apply these methods to the corresponding case of distributions in multiple variables.
In this paper, we obtain optimal upper bounds for all the Neumann eigenvalues in two situations (that are closely related). First we consider a one-dimensional Sturm–Liouville eigenvalue problem where the density is a function h(x) whose some power is concave. We prove existence of a maximizer for (mu _k(h)) and we completely characterize it. Then we consider the Neumann eigenvalues (for the Laplacian) of a domain (Omega subset {mathbb {R}}^d) of given diameter and we assume that its profile function (defined as the (d-1) dimensional measure of the slices orthogonal to a diameter) has also some power that is concave. This includes the case of convex domains in ({mathbb {R}}^d), containing and generalizing previous results by P. Kröger. On the other hand, in the last section, we give examples of domains for which the upper bound fails to be true, showing that, in general, (sup D^2(Omega )mu _k(Omega )= +infty ).
Bleher et al. began studying higher codimension Iwasawa theory for classical Iwasawa modules. Subsequently, Lei and Palvannan studied an analogue for elliptic curves with supersingular reduction. In this paper, we obtain a vast generalization of the work of Lei and Palvannan. A key technique is an approach to the work of Bleher et al. that the author previously proposed. For this purpose, we also study the structure of ±-norm subgroups and duality properties of multiply-signed Selmer groups.
Let p be a rational prime, let F denote a finite, unramified extension of (mathbb {Q}_p), let K be the completion of the maximal unramified extension of (mathbb {Q}_p), and let (overline{K}) be some fixed algebraic closure of K. Let A be an abelian variety defined over F, with good reduction, let (mathcal {A}) denote the Néron model of A over (textrm{Spec}(mathcal {O}_F)), and let (widehat{mathcal {A}}) be the formal completion of (mathcal {A}) along the identity of its special fiber, i.e. the formal group of A. In this work, we prove two results concerning the ramification of p-power torsion points on (widehat{mathcal {A}}). One of our main results describes conditions on (widehat{mathcal {A}}), base changed to (text {Spf}(mathcal {O}_K) ), for which the field (K(widehat{mathcal {A}}[p])/K) i s a tamely ramified extension where (widehat{mathcal {A}}[p]) denotes the group of p-torsion points of (widehat{mathcal {A}}) over (mathcal {O}_{overline{K}}). This result generalizes previous work when A is 1-dimensional and work of Arias-de-Reyna when A is the Jacobian of certain genus 2 hyperelliptic curves.
In this paper, we develop an integral refinement of the Perrin-Riou theory of exponential maps. We also formulate the Perrin-Riou theory for anticyclotomic deformation of modular forms in terms of the theory of the Serre–Tate local moduli and interpolate generalized Heegner cycles p-adically.
We classify the (({mathfrak {g}},K))-modules generated by nearly holomorphic Hilbert–Siegel modular forms by the global method. As an application, we study the image of projection operators on the space of nearly holomorphic Hilbert–Siegel modular forms with respect to infinitesimal characters in terms of (({mathfrak {g}},K))-modules.
Let (pge 5) be a prime. We construct modular Galois representations for which the (mathbb {Z}_p)-corank of the p-primary Selmer group (i.e., its (lambda )-invariant) over the cyclotomic (mathbb {Z}_p)-extension is large. More precisely, for any natural number n, one constructs a modular Galois representation such that the associated (lambda )-invariant is (ge n). The method is based on the study of congruences between modular forms, and leverages results of Greenberg and Vatsal. Given a modular form (f_1) satisfying suitable conditions, one constructs a congruent modular form (f_2) for which the (lambda )-invariant of the Selmer group is large. A key ingredient in acheiving this is the Galois theoretic lifting result of Fakhruddin–Khare–Patrikis, which extends previous work of Ramakrishna. The results are illustrated by explicit examples.
Let K be an imaginary quadratic field and (K_infty ) be the ({textbf{Z}}_p^2)-extension of K. Answering a question of Ahmed and Lim, we show that the Pontryagin dual of the Selmer group over (K_infty ) associated to a supersingular polarized abelian variety admits an algebraic functional equation. The proof uses the theory of (Gamma )-system developed by Lai, Longhi, Tan and Trihan. We also show the algebraic functional equation holds for Sprung’s chromatic Selmer groups of supersingular elliptic curves along (K_infty ).
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：