相关论文: Mass formulas for local Galois representations and…

We develop the motivic integration theory over formal Deligne-Mumford stacks over a power series ring of arbitrary characteristic. This is a generalization of the corresponding theory for tame and smooth Deligne-Mumford stacks constructed…

Bhargava has given a formula, derived from a formula of Serre, computing a certain count of extensions of a local field, weighted by conductor and by number of automorphisms. We interpret this result as a counting formula for permutation…

We prove motivic versions of mass formulas by Krasner, Serre and Bhargava concerning (weighted) counts of extensions of local fields.

The quotient of a finite-dimensional vector space by the action of a finite subgroup of automorphisms is usually a singular variety. Under appropriate assumptions, the McKay correspondence relates the geometry of nice resolutions of…

We prove a version of the wild McKay correspondence by using $p$-adic measures. This result provides new proofs of mass formulas for extensions of a local field by Serre, Bhargava and Kedlaya.

We propose an arithmetic McKay correspondence which relates suitably defined zeta functions of some Deligne-Mumford stacks to the zeta functions of their crepant resolutions. Some examples are discussed.

We discuss how the motivic integration will be generalized to wild Deligne-Mumford stacks, that is, stabilizers may have order divisible by the characteristic of the base or residue field. We pose several conjectures on this topic. We also…

Bhargava proved a formula for counting, with certain weights, degree n etale extensions of a local field, or equivalently, local Galois representations to S_n. This formula is motivation for his conjectures about the density of…

We prove some new cases of local--global compatibility for the Galois representations associated to Hilbert modular forms of low weight (that is, partial weight one).

A total mass is the weighted count of continuous homomorphisms from the absolute Galois group of a local field to a finite group. In the preceding paper, the authors observed that in a particular example, two total masses coming from two…

We analyze the weight diagram associated with foliations on the complex projective plane through the Hilbert-Mumford criterion in Geometric Invariant Theory, focusing in particular on invariants such as the algebraic multiplicity and the…

We study the images of tautological bundles on Hilbert schemes of points on surfaces and their wedge powers under the derived McKay correspondence. The main observation of the paper is that using a derived equivalence differing slightly…

The Hilbert space of level $q$ Chern-Simons theory of gauge group $G$ of the ADE type quantized on $T^2$ can be represented by points that lie on the weight lattice of the Lie algebra $\mathfrak{g}$ up to some discrete identifications. Of…

We extend the modularity lifting result of the arXiv:1111.2804 to allow Galois representations with some ramification at p. We also prove modularity mod 2 and 5 of certain Galois representations. We use these results to prove many new cases…

We establish a correspondence between orbifold and singular elliptic genera of a global quotient. While the former is defined in terms of the fixed point set of the action, the latter is defined in terms of the resolution of singularities.…

We study the McKay correspondence for representations of the cyclic group of order $p$ in characteristic $p$. The main tool is the motivic integration generalized to quotient stacks associated to representations. Our version of the change…

In positive characteristic, there exist counterexamples to the statement corresponding to Batyrev's theorem concerning the McKay correspondence. In this paper, we give another computation of the counterexamples by using stringy-point count…

This article addresses the problem of existence of local factors, i.e., the root numbers and L-functions attached to representations of reductive groups over local fields and irreducible finite dimensional representations of their L-groups,…

We consider the p-adic Galois representation associated to a Hilbert modular form. We show the compatibility with the local Langlands correspondence at a place divising p under a certain assumption. We also prove the monodromy-weight…

We propose a new model for counting $\mathbf{GL}_2(\mathbb{F}_p)$-number fields having the same local properties as the splitting field of the mod $p$-Galois representation associated with an elliptic curve over the rational numbers. We…