Related papers: Augmentation du niveau pour U(3) (Level-Raising fo…

We introduce the universal unitarily graded A-algebra for a commutative ring A and an arbitrary abelian extension U of the group of units of A, and use this concept to give simplified proofs of the main theorems of co-Galois theory in the…

We prove an effective version of the inverse theorem for the Gowers $U^3$-norm for functions supported on high-rank quadratic level sets in finite vector spaces. For configurations controlled by the $U^3$-norm (complexity-two…

Using $l$-adic completed cohomology in the context of Shimura varieties of Kottwitz-Harris-Taylor type attached to some fixed similitude group $G$, we prove, allowing to increase the levet at $l$, some new automorphic congruences between…

In this paper, we give an equivalent condition for an abelian variety over a finite field to have multiplication by a quaternion algebra over a number field. We prove the result by combining Tate's classification of the endomorphism…

We construct level-raising congruences between $p$-ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the $n^\text{th}$…

We discuss the phase structure and the equation of state for QCD at non-zero temperature and density. Derivatives of $\ln Z$ with respect to quark chemical potential $\mu_q$ up to fourth order are calculated for 2-flavor QCD, enabling…

Let $A$ be a separable amenable $C^*$-algebra and $B$ a non-unital and $\sigma$-unital simple $C^*$-algebra with continuous scale ($B$ need not be stable). We classify, up to unitary equivalence, all essential extensions of the form $0…

We construct liftings of reduction maps from CM points to supersingular points for general quaternion algebras and use these liftings to establish a precise correspondence between CM points on indefinite quaternion algebras with a given…

We obtain a lifting property for finite quotients of algebraic groups, and applications to the structure of these groups.

We prove a p-adic Labesse-Langlands transfer from the group of units in a definite quaternion algebra to its subgroup of norm one elements. More precisely, given an eigenvariety for the first group, we show that there exists an eigenvariety…

We prove a companion forms theorem for ordinary n-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author, and a technique for deducing companion forms theorems due to the first…

The purpose of this paper is to show that the reflex fields of a given CM-field is equipped with a certain combinatorial structure that has not been exploited yet. We prove three theorems using this structure; the first theorem is on the…

Let $A$ be a unital separable amenable \CA and $C$ be a unital \CA with certain infinite property. We show that two full monomorphisms $h_1, h_2: A\to C$ are approximately unitarily equivalent if and only if $[h_1]=[h_2]$ in $KL(A,C).$ Let…

A version of Auslander theorem is proven for the following classes of noncommutative algebras: (a) noetherian PI local (or connected graded) algebras of finite injective dimension, (b) universal enveloping algebras of finite dimensional Lie…

Under hypotheses required for the Taylor-Wiles method, we prove for forms of $U(3)$ which are compact at infinity that the lattice structure on upper alcove algebraic vectors or on principal series types given by the $\lambda$-isotypic part…

We analyze general convergence properties of the Taylor expansion of observables to finite chemical potential in the framework of an effective 2+1 flavor Polyakov-quark-meson model. To compute the required higher order coefficients a novel…

We develop a graphical method for computing the virial expansion coefficients for a nonrelativistic quantum field theory. As an example we compute the third virial coefficient b3 for unitary fermions, a nonperturbative system. By…

By Liouville's theorem, in dimensions 3 or more conformal transformations form a finite-dimensional group, an apparent drastic departure from the 2-dimensional case. We propose a derived enhancement of the conformal Lie algebra which is an…

We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms.

In this paper a fourth order equation involving critical growth is considered under Navier boundary condition. We give some topological conditions on a given function to ensure the existence of solutions. Our methods involve the study of…