arXiv subjects

Katsuyuki Bando

Publications and source records attributed to Katsuyuki Bando.

7 recordsLinked to original sources

arXiv2026

Geometric Satake equivalence in mixed characteristic and Springer correspondence

The geometric Satake equivalence and the Springer correspondence are closely related when restricting to small representations of the Langlands dual group. We prove this result for étale sheaves, including the case of the mixed characteristic affine Grassmannian, assuming a sufficient ramification. In this process, we construct a monoidal structure on the restriction functor of Satake categories. We construct also a canonical isomorphism between a mixed characteristic affine Grassmannian under a sufficient ramification and an equal characteristic one.

math.NT↗

arXiv2026

Relation between the two geometric Satake equivalence via nearby cycle

Fargues and Scholze proved the geometric Satake equivalence over the Fargues--Fontaine curve. On the other hand, Zhu proved the geometric Satake equivalence using a Witt vector affine Grassmannian. In this paper, we explain the relation between the two version of the geometric Satake equivalence via nearby cycle.

math.NT↗

arXiv2026

Two monoidal structures on Satake category in mixed characteristic

Fargues and Scholze proved the geometric Satake equivalence over the Fargues-Fontaine curve. This can be transferred to the geometric Satake equivalence concerning a Witt vector affine Grassmannian via nearby cycle. On the other hand, Zhu proved the geometric Satake equivalence concerning a Witt vector affine Grassmannian. In this paper, we explain the coincidence of these two geometric Satake equivalences, including the coincidence of the two symmetric monoidal structures on the Satake category.

math.NT↗

arXiv2026

Derived geometric Satake equivalence on the Beilinson-Drinfeld Grassmannian with one leg in mixed characteristic

Fargues-Scholze developed a framework for the geometric Langlands program on the Fargues-Fontaine curve. In particular, they proved the geometric Satake equivalence on the moduli space of closed Cartier divisors on the curve. We prove the derived version of this equivalence with one leg. Namely, we show that the derived category of etale sheaves on the local Hecke stack is equivalent to the category of L-group-equivariant perfect complexes over the symmetric algebra of the shifted and (-1)-Tate-twisted Lie algebra.

math.NT↗

arXiv2024

On the Complexity of Interpolation by Polynomials with Non-negative Real Coefficients

In this paper, we consider interpolation by \textit{completely monotonous} polynomials (CMPs for short), that is, polynomials with non-negative real coefficients. In particular, given a finite set $S\subset \mathbb{R}_{>0} \times \mathbb{R}_{\geq 0}$, we consider \textit{the minimal polynomial} of $S$, introduced by Berg [1985], which is `minimal,' in the sense that it is eventually majorized by all the other CMPs interpolating $S$. We give an upper bound of the degree of the minimal polynomial of $S$ when it exists. Furthermore, we give another algorithm for computing the minimal polynomial of given $S$ which utilizes an order structure on sign sequences. Applying the upper bound above, we also analyze the computational complexity of algorithms for computing minimal polynomials including ours.

math.NA↗

arXiv2024

Derived Satake category and Affine Hecke category in mixed characteristics

We construct a new affine Grassmannian which connects an equal characteristic affine Grassmannian and Zhu's Witt vector affine Grassmannian. As a result, we deduce the mixed characteristic version of the Bezrukavnikov-Finkelberg's derived Satake equivalence. By the same argument, we also obtain the mixed characteristic version of the Bezrukavnikov's equivalence between two categorifications of an affine Hecke algebra.

math.NT↗

arXiv2020

Foundations of Temperature Theory

Temperature of combinatorial games have been long studied since when Conway established the modern combinatorial game theory, and there are several variations of the concepts. In this article, we focus on one of the classical versions of temperature, and give precise proofs to the fundamental claims on temperature, namely, the existence, order-preservation, and homomorphism. Besides, a general relationship between the value and the thermograph of a game is investigated.

math.CO↗