We investigate the quantization problem of $(-1)$-shifted derived Poisson manifolds in terms $\BV_\infty$-operators on space Berezinian half-densities. prove that quantizing such a manifold is equivalent to lifting consecutive sequences Maurer-Cartan elements short exact differential graded Lie algebras, where obstruction certain class second cohomology. Consequently, quantizable if cohomology ...

Let Γg,n, for 2g − 2 + n > 0, be the Teichmüller group of an n-punctured genus g compact Riemann surface Sg,n and let Γ(l), for a prime l ≥ 2, be the abelian level defined by the kernel of the natural representation Γg,n → Sp2g(Z/l). The pro-l completion Γ(l)(l) of Γ(l) defines a profinite completion of Γg,n, which we call the relative pro-l completion and denote by Γ (l) g,n. There is a natura...

Let R be any ring (with 1), G a torsion free group and RG the corresponding group ring. Let Ext∗RG(M,M) be the cohomology ring associated to the RG-module M . Let H be a subgroup of finite index of G. The following is a special version of our main Theorem: Assume the profinite completion of G is torsion free. Then an element ζ ∈ Ext∗RG(M,M) is nilpotent (under Yoneda’s product) if and only if i...

1 Introduction 1.1. Let G be a connected reductive group over Q. Diamond [16] and Fujiwara [27] (independently) have axiomatized the Taylor-Wiles method which allows to study some local components T m of a Hecke algebra T for G of suitable (minimal) level; when it applies, this method shows at the same time that T m is complete intersection and that some cohomology module, viewed as T-module, i...

Let G be a nite group and k an algebraically closed eld of characteristic p. Let F U be the Rickard idempotent kG-module corresponding to the set U of subvarieties of the cohomology variety VG which are not irreducible components. We show that F U is a nite sum of generic modules corresponding to the irreducible components of VG. In this context, a generic module is an indecomposable module of ...

We give a new proof of a polynomial identity involving the minors of a matrix, that originated in the study of integer torsion in a local cohomology module.

Part I of this paper develops various general concepts in generic representation and cohomology theories. Roughly speaking, we provide a general theory of orders in non-semisimple algebras applicable to problems in the representation theory of nite and algebraic groups, and we formalize the notion of a \generic" property in representation theory. Part II makes new contributions to the non-descr...

An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.