Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...

Let π be a cuspidal generic representation of SO(2n + 1,A). We prove that L(12 , π) ≥ 0.

In [Shepherd-Barron and Taylor 97] it is shown that for = 3 and 5 every odd, irreducible, two-dimensional Galois representation of Gal(Q̄/Q) with values in F and determinant the cyclotomic character is “elliptic,” i.e., it agrees with the representation given by the action of Gal(Q̄/Q) on the -torsion points of an elliptic curve defined over Q. In this note we will show that this is false for eve...

Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

For any unitary cuspidal representations πn of GLn(QA), n = 2, 3, 4, respectively, consider two automorphic representations Π and Π of GL6(QA), where Πp ∼= ∧π4,p for p 6= 2, 3 and π4,p not supercuspidal, and Π = π2 π3. First, Hypothesis H for Π and Π is proved. Then contributions from prime powers are removed from the prime number theorem for cuspidal representations π and π of GLm(QA) and GLm′...

We prove the cleanness of cuspidal character sheaves in arbitrary characteristic in the few cases where it was previously unknown. 2010 Math. Subj. Class. 20G99.