We study the growth of p-primary fine Selmer group, R(E/F ′ ), an elliptic curve over intermediate sub-extension F a p-adic Lie extension, ℒ/F. estimate ℤ p -corank kernel and cokernel restriction map r ℒ/F :R(E/F )→R(E/ℒ) Gal(ℒ/F ) with finite extension contained in ℒ. show that groups these is related to structure group infinite level. On specializing certain (possibly non-commutative) extens...

A bstract We study the defect groups of $$ {D}_p^b D p b ( G ) theories using geometric engineering and BPS quivers. In simple case when b = h ∨ ), we use quivers theory to see that group is compatible with a known Maruyoshi-Song flow. To extend w...

We show that the birationality class of a quadric surface bundle over $\mathbb{P}^2$ is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality very general bundles with discriminant curves fixed degree. In particular, construct explicit models these for some data. Among others, obtain various birational nodal Gushel-Mukai fourfold, as well cubic fourfold...

We introduce a notion of an integral along bimonoid homomorphism as simultaneous generalization the and cointegral bimonoids. The purpose this paper is to characterize existence specific integral, called normalized generator in terms kernel cokernel homomorphism. volume on abelian category dimension vector spaces order groups. In applications, we show that there exists nontrivial partially defi...

Let G be a complex simply connected semisimple Lie group and let Γ torsionless uniform irreducible lattice in G. Then Γ﹨G is compact non-Kähler manifold whose tangent bundle holomorphically trivial. In this note we compute the Picard of when rank(G)≥3. When rank(G)<3, determine Pic0(Γ﹨G)⊂Pic(Γ﹨G) topologically trivial holomorphic line bundles. rank(G)≥2, also show that Pic0(PΓ) isomorphic to Pi...

Let F be a field of characteristic zero and let ft,n be the stabilization homomorphism Hn(SLt(F ), Z) → Hn(SLt+1(F ), Z). We prove the following results: For all n, ft,n is an isomorphism if t ≥ n + 1 and is surjective for t = n, confirming a conjecture of C-H. Sah. Furthermore if n is odd, then fn,n is an isomorphism. If n ≥ 1 is even then the cokernel of fn−1,n is naturally isomorphic to the ...

Abstract Let $${\mathbb {A}}$$ A be a 2-category with suitable opcomma objects and pushouts. We give direct proof that, provided that the codensity monad of morphism p exists is preserved by morphism, factorization given lax descent object two-dimensional cokernel diagram up to isomorphism same as semantic , ...

A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a stratified space, giving stratifications over a set of resolution levels. We then use methods derived from kernel and cokernel persistent homology to cluster...

Let the manifold X parametrise a family of compact complex submanifolds of the complex (or CR) manifold Z. Under mild conditions the Penrose transform typically provides isomorphisms between a cohomology group of a holomorphic vector bundle V → Z and the kernel of a differential operator between sections of vector bundles over X. When the spaces in question are homogeneous for a group G the Pen...