Related papers: Arithmetic models for Shimura varieties
Recently Iwasawa theory for graphs is developing. A significant achievement includes an analogue of Iwasawa class number formula, which describes the asymptotic growth of the numbers of spanning trees for $\mathbb{Z}_p$-coverings of graphs.…
This note reviews our mathematical models for fish schooling, considered in free space, and in space with obstacle and food resource. These models are performed by stochastic differential equations or stochastic partial differential…
We give a proposal for future development of the model theory of valued fields. We also summarize some recent results on p-adic numbers.
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
We prove a Cherednik style $p$-adic uniformization theorem for Shimura varieties associated to certain groups of unitary similitudes of size two over totally real fields. Our basic tool is the alternative modular interpretation of the…
We consider the problem of defining an action of Hecke operators on the coherent cohomology of certain integral models of Shimura varieties. We formulate a general conjecture describing which Hecke operators should act integrally and solve…
We introduce a new construction of towers of algebraic curves over finite fields and provide a simple example of an optimal tower.
We explore several variations on the recently discovered phenomena of murmurations for elliptic curves and modular forms.
We construct classes in the middle degree plus one motivic cohomology of the Siegel Shimura variety of almost any dimension. We compute their image by Beilinson's higher regulator in terms of Rankin-Selberg type automorphic integrals. Our…
In this review, we examine the recent progress in saliency prediction and proposed several avenues for future research. In spite of tremendous efforts and huge progress, there is still room for improvement in terms finer-grained analysis of…
In these notes I proved the Chai-Faltings version of Eichler-Shimura congruence relation for simple GSpin Shimura varieties. This extends the results by Bueltel, Wedhorn and Koskivirta.
We construct a family of special cycle classes on the regular integral model of an orthogonal Shimura variety, and show that these cycle classes appear as Fourier coefficients of a Siegel modular form. Passing to the generic fiber of the…
We study the characters induced by suitable level structures of abelian varieties with quaternionic multiplication following the methods of Mazur, Momose, who studied the characters induced by elliptic curves, and Arai--Momose, who studied…
Level $m$-stratifications on PEL Shimura varieties are defined and studied by Wedhorn using BT-$m$s with PEL structure, and then by Vasiu for general Hodge type Shimura varieties using Shimura $F$-crystals. The theory of foliations is…
Different kinds of models are used to study various natural and technical phenomena. Usually, the researcher is limited to using a certain kind of model approach, not using others (or even not realizing the existence of other model…
We study the Kuramoto model with attractive sine coupling. We introduce a complex-valued matrix formulation whose argument coincides with the original Kuramoto dynamics. We derive an exact solution for the complex-valued model, which…
These are notes from talks of the authors on some explicit examples of families of Calabi-Yau threefolds which are parametrised by a Shimura variety. We briefly review the periods of Calabi-Yau threefolds and we discuss a recent result on…
In this paper, we study special cycles on the basic locus of certain unitary Shimura varieties over the ramified primes and their local analogues on the corresponding Rapoport-Zink spaces. We study the support and compute the dimension of…
This paper describes work carried out on a model for the evolution of graph classes in complex objects. By defining evolution rules and propagation strategies on graph classes, we aim to define a user-definable means to manage data…
This paper presents a study on the advancement of computational models for the analysis of illicit activities. Computational models are being adapted to address a number of social problems since the development of computers. Computational…