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We investigate the Brauer class of the endomorphism algebra of the motive attached to a non-CM form. The ramification of the algebra is shown in many cases to be controlled by the normalized slopes of the form.

In this paper we present a classification of the possible upper ramification jumps for an elementary abelian p-extension of a p-adic field. The fundamental step for the proof of the main result is the computation of the ramification…

Let X --> P^2 be a p-cyclic cover branched over a smooth, connected curve C of degree divisible by p, defined over a separably closed field of prime-to-p characteristic. We show that all (unramified) p-torsion Brauer classes on X that are…

Let G be a semisimple affine algebraic group of inner type over a field F. We write C for the class of all finite direct products of projective G-homogeneous F-varieties. We determine the structure of the Chow motives with coefficients in a…

Let $E$ be a field satisfying the following conditions: (i) the $p$-component of the Brauer group Br$(E)$ is nontrivial whenever $p$ is a prime number for which $E$ is properly included in its maximal $p$-extension; (ii) the relative Brauer…

We study the $S$-arithmetic (co)homology of reductive groups over number fields with coefficients in (duals of) certain locally algebraic and locally analytic representations for finite sets of primes $S$. We use our results to construct…

We study algebra endomorphisms and derivations of some localized down-up algebras $\A$. First, we determine all the algebra endomorphisms of $\A$ under some conditions on $r$ and $s$. We show that each algebra endomorphism of $\A$ is an…

We show how the ramification filtration on the maximal elementary abelian p-extension (p prime) on a local number field of residual characteristic p can be derived using only Kummer theory and a certain orthogonality relation for the Kummer…

We consider the class of complete discretely valued fields such that the residue field is of prime characteristic p and the cardinality of a $p$-base is 1. This class includes two-dimensional local and local-global fields. A new definition…

It is shown that the multiplicative monoids of Temperley-Lieb algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a self-adjunction is found in a…

In this article we study in detail the category of noncommutative motives of separable algebras Sep(k) over a base field k. We start by constructing four different models of the full subcategory of commutative separable algebras CSep(k).…

A new class of associative algebras referred to as affine walled Brauer algebras are introduced. These algebras are free with infinite rank over a commutative ring containing 1. Then level two walled Brauer algebras over C are defined,…

We study irreducible mod p representations, valued in general reductive groups, of the Galois group of a number field. When the number field is totally real, we show that odd representations satisfying local ramification hypotheses and a…

The class of UMP algebras arises in several classification problems in the context of derived categories of finite-dimensional algebras. In this paper we define the class of UMP algebras and develop algebraic combinatorics tools in order to…

In this paper we examine the behavior of lifts of Brauer characters in p-solvable groups where p is an odd prime. In the main result, we show that if \phi \in IBrp(G) is a Brauer character of a solvable group such that \phi has an abelian…

Let A, A' be two central simple algebras over a field F and \mathbb{F} be a finite field of characteristic p. We prove that the upper indecomposable direct summands of the motives of two anisotropic varieties of flags of right ideals…

This paper generalises previous work of the author to the setting of overconvergent $p$-adic automorphic forms for a definite quaternion algebra over a totally real field. We prove results which are analogues of classical `level raising'…

We prove that the Galois pseudo-representation valued in the mod $p^n$ cuspidal Hecke algebra for GL(2) over a totally real number field $F$, of parallel weight $1$ and level prime to $p$, is unramified at any place above $p$. The same is…

For a smooth proper variety over a $p$-adic field, the Brauer group and abelian fundamental group are related to the higher Chow groups by the Brauer-Manin pairing and the class field theory. We generalize this relation to smooth (possibly…

Given a prime $p \ge 5$ and an abstract odd representation $\rho_n$ with coefficients modulo $p^n$ (for some $n \ge 1$) and big image, we prove the existence of a lift of $\rho_n$ to characteristic $0$ whenever local lifts exist (under some…