Mathematische Zeitschrift最新文献

In this paper, we study periodicity phenomena for modular extensions between Weyl modules and between Weyl and simple modules of the general linear group that are associated to adding a power of the characteristic to the first parts of the involved partitions.

In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for the scales of Hajłasz–Triebel–Lizorkin and Hajłasz–Besov spaces in the general context of quasi-metric measure spaces for an optimal range of the smoothness parameter s. An interesting facet of this work is how the range of s for which the above characterizations of these embeddings hold is intimately linked (in a quantitative manner) to the geometric makeup of the underlying space. Importantly, although the main results in this article are stated in the context of quasi-metric spaces, the authors provide several examples illustrating how this range of s is strictly larger than similar ones currently appearing in the literature, even in the metric setting. Moreover, the authors relate these values of s to the (non)triviality of these function spaces.

In the present paper, we establish an analytic continuation of Drinfeld logarithms by using the techniques introduced in Furusho (Tunis J Math 4(3):559–586, 2022) . This result can be seen as an analogue of the analytic continuation of the elliptic integrals of the first kind for Drinfeld modules.

We study the average behaviour of the Iwasawa invariants for Selmer groups of elliptic curves, considered over anticyclotomic (mathbb {Z}_p)-extensions in both the definite and indefinite settings. The results in this paper lie at the intersection of arithmetic statistics and Iwasawa theory.

We use the p-divisible group attached to a 1-motive to generalize the conjugate p-adic uniformization of Iovita–Morrow–Zaharescu to arbitrary p-adic formal semi-abelian schemes or p-divisible groups over the ring of integers in a p-adic field. This mirrors a mixed Hodge theory construction of the inverse uniformization map for complex semi-abelian varieties.

In this paper we introduce Morse Lie groupoid morphisms and study their main properties. We show that this notion is Morita invariant which gives rise to a well defined notion of Morse function on differentiable stacks. We show a groupoid version of the Morse lemma which is used to describe the topological behavior of the critical subgroupoid levels of a Morse Lie groupoid morphism around its nondegenerate critical orbits. We also prove Morse type inequalities for certain separated differentiable stacks and construct a Morse double complex whose total cohomology is isomorphic to the Bott–Shulman–Stasheff cohomology of the underlying Lie groupoid. We provide several examples and applications.

We introduce generalized Demazure operators for the equivariant oriented cohomology of the flag variety, which have specializations to various Demazure operators and Demazure–Lusztig operators in both equivariant cohomology and equivariant K-theory. In the context of the geometric basis of the equivariant oriented cohomology given by certain Bott–Samelson classes, we use these operators to obtain formulas for the structure constants arising in different bases. Specializing to divided difference operators and Demazure operators in singular cohomology and K-theory, we recover the formulas for structure constants of Schubert classes obtained in Goldin and Knutson (Pure Appl Math Q 17(4):1345–1385, 2021). Two specific specializations result in formulas for the the structure constants for cohomological and K-theoretic stable bases as well; as a corollary we reproduce a formula for the structure constants of the Segre–Schwartz–MacPherson basis previously obtained by Su (Math Zeitschrift 298:193–213, 2021). Our methods involve the study of the formal affine Demazure algebra, providing a purely algebraic proof of these results.

It is known that the notion of a transitive subgroup of a permutation group G extends naturally to subsets of G. We consider subsets of the general linear group ({{,textrm{GL},}}(n,q)) acting transitively on flag-like structures, which are common generalisations of t-dimensional subspaces of (mathbb {F}_q^n) and bases of t-dimensional subspaces of (mathbb {F}_q^n). We give structural characterisations of transitive subsets of ({{,textrm{GL},}}(n,q)) using the character theory of ({{,textrm{GL},}}(n,q)) and interpret such subsets as designs in the conjugacy class association scheme of ({{,textrm{GL},}}(n,q)). In particular we generalise a theorem of Perin on subgroups of ({{,textrm{GL},}}(n,q)) acting transitively on t-dimensional subspaces. We survey transitive subgroups of ({{,textrm{GL},}}(n,q)), showing that there is no subgroup of ({{,textrm{GL},}}(n,q)) with (1<t<n) acting transitively on t-dimensional subspaces unless it contains ({{,textrm{SL},}}(n,q)) or is one of two exceptional groups. On the other hand, for all fixed t, we show that there exist nontrivial subsets of ({{,textrm{GL},}}(n,q)) that are transitive on linearly independent t-tuples of (mathbb {F}_q^n), which also shows the existence of nontrivial subsets of ({{,textrm{GL},}}(n,q)) that are transitive on more general flag-like structures. We establish connections with orthogonal polynomials, namely the Al-Salam–Carlitz polynomials, and generalise a result by Rudvalis and Shinoda on the distribution of the number of fixed points of the elements in ({{,textrm{GL},}}(n,q)). Many of our results can be interpreted as q-analogs of corresponding results for the symmetric group.

In this paper, we are concerned with the study of the following 2-D Schrödinger–Poisson equation with critical exponential growth

where (varepsilon >0) is a parameter, (I_alpha ) is the Riesz potential, (0<alpha <2), (Vin {mathcal {C}}({{mathbb {R}}}^2,{{mathbb {R}}})), and (fin {mathcal {C}}({{mathbb {R}}},{{mathbb {R}}})) satisfies the critical exponential growth. By variational methods, we first prove the existence of ground state solutions for the above system with the periodic potential. Then we obtain that there exists a positive ground state solution of the above system concentrating at a global minimum of V in the semi-classical limit under some suitable conditions. Meanwhile, the exponential decay of this ground state solution is detected. Finally, we establish the multiplicity of positive solutions by using the Ljusternik–Schnirelmann theory.

We provide a characterization of when a coarse equivalence between coarse disjoint unions of expander graphs is close to a bijective coarse equivalence. We use this to show that if the uniform Roe algebras of coarse disjoint unions of expanders graphs are isomorphic, then the metric spaces must be bijectively coarsely equivalent.