Related papers: Special cycles on orthogonal Shimura varieties

A finite shift plane can be equivalently defined via abelian relative difference sets as well as planar functions. In this paper, we present a generic way to construct unitals in finite shift planes of odd orders $q^2$. We investigate…

This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include…

We study algebraic cycles on complex Gushel-Mukai (GM) varieties. We prove the generalised Hodge conjecture, the (motivated) Mumford-Tate conjecture, and the generalised Tate conjecture for all GM varieties. We compute all integral Chow…

Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in…

We consider the cycle structure of a random permutation $\sigma$ chosen uniformly from the symmetric group, subject to the constraint that $\sigma$ does not contain cycles of length exceeding $r.$ We prove that under suitable conditions the…

The paper is a continuation of the paper of Kudla-Rapoport-Zink on $p$-adic uniformization of Shimura curves associated to a group of binary unitary similitudes. Here we consider two variants: first, the RSZ variant, for which we can allow…

Given our set-up of a system of curves and maps between them satisfying certain assumptions, we prove a classicality criterion for overconvergent sections of line bundles over these curves. As a result, we prove such criteria for…

We prove that the intersection cohomology of the Baily-Borel compactification of a complex Shimura variety is identified with the top weight quotient of the mixed Hodge structure on the reductive Borel-Serre compactification. This yields…

In previous work, we defined certain virtual fundamental classes for special cycles on the moduli stack of Hermitian shtukas, and related them to the higher derivatives of non-singular Fourier coefficients of Siegel-Eisenstein series. In…

We introduce the notion of Mukai regularity (M-regularity) for coherent sheaves on abelian varieties. The definition is based on the Fourier-Mukai transform, and in a special case depending on the choice of a polarization it parallels and…

This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. Under an abstract setting, we establish the existence of bistable traveling waves for discrete and continuous-time monotone semiflows.…

We study the prime-to-$p$ Hecke action on the projective limit of the sets of connected components of Shimura varieties with fixed parahoric or Bruhat--Tits level at $p$. In particular, we construct infinitely many Shimura varieties for CM…

We develop a new methodology to contract tensor networks within the corner transfer matrix renormalization group approach for a wide range of two-dimensional lattice geometries. We discuss contraction algorithms on the example of…

Local models are certain schemes, defined in terms of linear-algebraic moduli problems, which give \'etale-local neighborhoods of integral models of certain p-adic PEL Shimura varieties defined by Rapoport and Zink. When the group defining…

In this paper we describe orbits of automorphism group on a horospherical variety in terms of degrees of homogeneous with respect to natural grading locally nilpotent derivations. In case of (may be non-normal) toric varieties a description…

In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations.…

For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…

In this paper, we study the basic locus in the fiber at $p$ of a certain unitary Shimura variety with a certain parahoric level structure. The basic locus $\widehat{\mathcal{M}^{ss}}$ is uniformized by a formal scheme $\mathcal{N}$ which is…

We establish some weighted $L^2$ inequalities for Fourier extension operators in the setting of orthonormal systems. In the process we develop a direct approach to such inequalities based on generalised Wigner distributions, complementing…

We establish new upper bounds about symmetric bilinear complexity in any extension of finite fields. Note that these bounds are not asymptotical but uniform. Moreover we give examples of Shimura curves that do not descend over their field…