The classical Gelfand–Naimark theorems provide important insight into the structure of general and of commutative -algebras. It is shown that these can be generalized to certain ordered -algebras. More precisely, for -bounded closed ordered -algebras, …
We study generators of the fundamental group of the group of symplectomorphisms for some particular symplectic forms. It was observed by Kȩdra (2009, Archivum Mathematicum 45) that there are many symplectic 4-manifolds , where M is neither rational no…
Let G be a p-adic classical group. The representations in a given Bernstein component can be viewed as modules for the corresponding Hecke algebra—the endomorphism algebra of a pro-generator of the given component. Using Heiermann’s construction of the…
In this paper, we prove results about solutions of the Diophantine equation over various number fields using the modular method. First, by assuming some standard modularity conjecture, we prove an asymptotic result for general number fields of narrow …
We show that all self-adjoint extensions of semibounded Sturm–Liouville operators with limit-circle endpoint(s) can be obtained via an additive singular form-bounded self-adjoint perturbation of rank equal to the deficiency indices, say . This characte…
In Aizenbud et al. (2010, Annals of Mathematics 172, 1407–1434), a multiplicity one theorem is proved for general linear groups, orthogonal groups, and unitary groups (
and U) over p-adic local fields. That is to say that when we have a pair of …
We consider a quiver with potential (QP) and an iced quiver with potential (IQP) associated with a Postnikov Diagram D and prove that their mutations are compatible with the geometric exchanges of D. This ensures that we may define a QP and an IQP …
We compute the generator rank of a subhomogeneous -algebra in terms of the covering dimension of the pieces of its primitive ideal space corresponding to irreducible representations of a fixed dimension. We deduce that every -stable approximately subho…
Let F be a totally real field, and let
be a CM quadratic extension. We construct a p-adic L-function attached to Hida families for the group
. It is characterized by an exact interpolation property for critical Rankin–Selberg L-values, at …
Let K be a number field. For which primes p does there exist an elliptic curve
admitting a K-rational p-isogeny? Although we have an answer to this question over the rationals, extending this to other number fields is a fundamental open problem…