相关论文: On mixed-$\omega$-sheaves

This paper is essentially made of the three preprints arXiv:1212.5818, arXiv:1311.0187, arXiv:1603.07876 gathered in a single text, with simplified proofs. We recall several results of the microlocal theory of sheaves of Kashiwara-Schapira…

We construct functorial Igusa stacks for all Hodge-type Shimura varieties, proving a conjecture of Scholze and extending earlier results of the fourth-named author for PEL-type Shimura varieties. Using the Igusa stack, we construct a sheaf…

We give several structure theorems for certain surjective endomorphisms on Mori fibre spaces, based on the dynamical Iitaka fibration of the ramification divisor. As an application, we prove the Kawaguchi-Silverman conjecture for projective…

We prove the Kakeya set conjecture for $\mathbb{Z}/N\mathbb{Z}$ for general $N$ as stated by Hickman and Wright [HW18]. This entails extending and combining the techniques of Arsovski [Ars21a] for $N=p^k$ and the author and Dvir [DD21] for…

We use twisted Fourier-Mukai transforms to study the relation between an abelian fibration on a holomorphic symplectic manifold and its dual fibration. Our reasoning leads to an equivalence between the derived category of coherent sheaves…

Using a mixed-characteristic incarnation of fusion, we prove an analog of Nekov\'a\v{r}-Scholl's plectic conjecture for local Shimura varieties. We apply this to obtain results on the plectic conjecture for (global) Shimura varieties after…

We generalize Koll\'ar's conjecture (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to Saito's $S$-sheaves twisted by a $\mathbb{Q}$-divisor. This gives a uniform treatment for various kinds of…

In this paper, we prove the bounded case of the Andre-Oort conjecture for special subvarieties in a mixed Shimura variety. This generalizes previous results of L. Clozel, E. Ullmo, and A. Yafaev. The proof is reduced to a special case of…

We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in…

We give a combinatorial proof of a natural generalization of the Murnaghan-Nakayama rule to loop Schur functions. We also define shifted loop Schur functions and prove that they satisfy a similar relation.

We introduce the notion of a Hodge-Riemann pair of cohomology classes that generalizes the classical Hodge-Riemann bilinear relations, and the notion of a Bogomolov pair of cohomology classes that generalizes the Bogomolov inequality for…

We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…

We consider Fujita's freeness conjecture in a relative setting and prove a criterion by proving a correct Q-divisor version of the Kollar vanishing theorem.

In this paper we prove restriction theorems for torsion-free sheaves that are (semi)stable with respect to the truncated Hilbert polynomial over a smooth projective variety. Our results apply in particular to Gieseker-semistable sheaves and…

The aim of this paper is to give a survey of the theory of bundle gerbes. In our approach we especially emphasize the unifying role of Morita equivalences in this theory. We also discuss a higher analog of Morita bundle gerbes called Morita…

In this note we propose an $\omega$-operadical way to prove the existence of the $\omega$-graph of the $\omega$-graphs and the reflexive $\omega$- graph of the reflexive $\omega$-graphs.

The theory of {\Gamma}-species is developed to allow species-theoretic study of quotient structures in a categorically rigorous fashion. This new approach is then applied to two graph-enumeration problems which were previously unsolved in…

In this paper, first we give a weak version of Ikeda's conjecture on the period of the Ikeda-Miyawaki lift. Next, we confirm this conjecture rigorously in some cases.

In this short note, we shall prove some observations regarding the connection between indestructible $\omega_1$-guessing models and the $\omega_1$-approximation property of forcing notions.

We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.