arXiv subjects

Yuta Takaya

Publications and source records attributed to Yuta Takaya.

6 recordsLinked to original sources

arXiv2026

On depth-zero integral models of local Shimura varieties

We specify explicit affinoids in depth-zero local Shimura varieties whose reductions are parabolic Deligne-Lusztig varieties, and construct explicit Jacquet-Langlands pairs of regular depth-zero supercuspidal representations in the cohomology of local Shimura varieties. Along the way, we develop the theory of integral moduli spaces of depth-zero level structures on local shtukas, especially at non-parahoric levels. As a consequence, we provide a direct construction of Yoshida's generalized semistable models of depth-zero Lubin-Tate spaces that were originally constructed as successive blowups.

math.NT↗

arXiv2026

Characteristic-free approaches around Yu's construction

We give a direct characteristic-free construction of twisted Heisenberg-Weil representations when there are no symmetric and ramified roots. As a consequence, we show that twisted Yu's construction naturally extends to residual characteristic $2$. Moreover, we give a geometric realization of such twisted Heisenberg-Weil representations via the Deligne-Lusztig construction for Heisenberg group schemes. As an application, we give an explicit description of positive-depth parahoric Deligne-Lusztig induction in the generic case.

math.RT↗

arXiv2026

Relative representability and parahoric level structures

We establish a representability criterion of $v$-sheaf theoretic modifications of formal schemes and apply this criterion to moduli spaces of parahoric level structures on local shtukas. In the proof, we introduce nice classes of equivariant profinite perfectoid covers and study geometric quotients of perfectoid formal schemes by profinite groups. As a corollary, we show the local representability of integral models of local Shimura varieties under hyperspecial levels, and study the forgetful morphisms between integral models of Shimura varieties associated with inclusions of parahoric subgroups under hyperspecial levels.

math.NT↗

arXiv2026

Categorification of local relative Langlands duality

We formulate the normalized period conjecture proposed by Ben-Zvi, Sakellaridis and Venkatesh in the framework of the categorical local Langlands correspondence and study its relation to distinction problems. Motivated by the work of Feng and Wang in the geometric setting, we verify the conjecture for the Iwasawa-Tate and Hecke periods, assuming the existence of the categorical local Langlands correspondence for $\mathrm{GL}_2$ with the Eisenstein compatibility.

math.RT↗

arXiv2025

Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic

We prove the equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic. This verifies a conjecture made by Rapoport and implies that the results of Nie and Zhou-Zhu can be extended to the whole irreducible components of affine Deligne-Lusztig varieties. The method is to translate the work of Hartl-Viehmann into mixed characteristic and construct local foliations for affine Deligne-Lusztig varieties. This leads us to develop a theory of formal algebraic geometry for perfect schemes.

math.AG↗

arXiv2024

Second adjointness and cuspidal supports at the categorical level

We prove the second adjointness in the setting of the categorical local Langlands correspondence. Moreover, we study the relation between Eisenstein series and cuspidal supports and present a conjectural characterization of irreducible smooth representations with supercuspidal $L$-parameters regarding geometric constant terms. The main technical ingredient is an induction principle for geometric Eisenstein series which allows us to reduce to the situations already treated in the literature.

math.RT↗