1. In this note we compute the cohomological obstruction to the existence of certain sheaves of vertex algebras on smooth varieties. These sheaves have been introduced and studied in the previous… (More)

Before we describe the result, let us explain some terminology and notation. For a smooth algebraic variety X , an algebra of cdo over X is by definition a Zariski sheaf V of Z≥0-graded vertex… (More)

In this note we discuss certain infinite subgroups of the Morava stabilizer groups and outline some applications in homotopy theory. 1. Description of the main result and its applications First we… (More)

We compute the cohomology of the Morava stabilizer group S2 at the prime 3 by resolving it by a free product Z/3∗Z/3 and analyzing the “relation module.”

We interpret the equivariant cohomology algebra H∗ GLn×C∗(T Fλ;C) of the cotangent bundle of a partial flag variety Fλ parametrizing chains of subspaces 0 = F0 ⊂ F1 ⊂ · · · ⊂ FN = C, dimFi/Fi−1 = λi,… (More)

In this note we will study the formal completion of the Jacobian of a certain class of curves over p-adic rings. These curves generalize the Legendre family of elliptic curves. As an immediate… (More)

We construct a spectral sequence that converges to the cohomology of the chiral de Rham complex over a Calabi-Yau hypersurface and whose first term is a vertex algebra closely related to the… (More)

Quantum Lie algebras (an important class of quadratic algebras arising in the Woronowicz calculus on quantum groups) are generalizations of Lie (super) algebras. Many notions from the theory of Lie… (More)

In this note we show that the positivity property of the equivariant signature of the loop space, first observed in [MS1] in the case of the even-dimensional pro-jective spaces, is valid for Picard… (More)