Related papers: Bloch-Kato exponential maps for local fields with …

This paper studies the Cohomological Donaldson-Thomas theory of loop stacks of $0$-shifted symplectic stacks. In particular, we compare $(-1)$-shifted tangent stacks of these moduli problems, which we view as additive, to loop stacks, which…

Let $K$ be a global or local field, $E/K$ a Galois extension, and Br$(E)$ the Brauer group of $E$. This paper shows that if $K$ is a local field, $v$ is its natural discrete valuation, $v'$ is the valuation of $E$ extending $v$, and $q$ is…

We continue our study of residual properties of mapping tori of free group endomorphisms. In this paper, we prove that each of these groups are virtually residually (finite $p$)-groups for all but finitely many primes$p$. The method…

Consider a unitary group $G(\mathbb{A}_{F^+})=U_{2r}(\mathbb{A}_{F^+})$ over a CM extension $F/F^+$ with $G(\mathbb{A}_\infty)$ compact. In this article, we study the Beilinson--Bloch--Kato conjecture for motives associated to irreducible…

We prove that the ramification filtration of the absolute Galois group of a comlete discrete valuation field with perfect residue field is characterized in terms of Fontaine's property (Pm).

This work presents author's explicit methods of constructing abelian extensions of complete discrete valuation fields. His approach to explicit equations of a cyclic extension of degree p^n which contains a given cyclic extension of degree…

Following Ribet's seminal 1976 paper there have been many results employing congruences between stable cuspforms and lifted forms to construct non-split extensions of Galois representations. We show how this strategy can be extended to…

This is a continuation of our previous work on the locally analytic vectors of the completed cohomology of modular curves. We construct differential operators on modular curves with infinite level at p in both "holomorphic" and…

A main problem in Galois theory is to characterize the fields with a given absolute Galois group. We apply a K-theoretic method for constructing valuations to study this problem in various situations. As a first application we obtain an…

We give necessary and sufficient conditions for a polynomially bounded o-minimal expansion of a real closed field (in a language of arbitrary cardinality) to be $\aleph_{\alpha}$-saturated. The conditions are in terms of the value group,…

We prove the modularity of minimally ramified ordinary residually reducible p-adic Galois representations of an imaginary quadratic field F under certain assumptions. We first exhibit conditions under which the residual representation is…

Let $\rho$ f,$\lambda$ be the residual Galois representation attached to a newform f and a prime ideal $\lambda$ in the integer ring of its coefficient field. In this paper, we prove explicit bounds for the residue characteristic of the…

In the present paper, we study the outer automorphism groups of the absolute Galois groups of 2-adic local fields from the point of view of anabelian geometry. Let us recall that it is well-known that the natural homomorphism from the…

Cubic and biquadratic reciprocity have long since been referred to as "the forgotten reciprocity laws", largely since they provide special conditions that are widely considered to be unnecessary in the study of number theory. In this…

We compare two maps that arise in study of the cohomology of number fields with ramification restricted to a finite set S of primes. One of these maps, which we call an S-reciprocity map, interpolates the values of cup products in…

We construct a variant of Karoubi's relative Chern character for smooth, separated schemes over the ring of integers in a p-adic field and prove a comparison with the rigid syntomic regulator. For smooth projective schemes we further relate…

We compute the mod $p$ cohomology algebra of a family of infinite discrete Kac-Moody groups of rank two defined over finite fields of characteristic different from $p$.

For all simple and finite extension of a valued field, we prove that its defect is the product of the effective degrees of the complete set of key polynomials associated. As a consequence, we obtain a local uniformization theorem for…

The aim of this paper is to extend some arithmetic results on elliptic modular forms to the case of Hilbert modular forms. Among these results let's mention : (1) the control of the image of the Galois representation modulo $p$, (2) Hida's…

The study of modular representation theory of the double covering groups of the symmetric and alternating groups reveals rich and subtle combinatorial and algebraic phenomena involving their irreducible characters and the structure of their…