On a symplectic manifold M , the quantum product defines a complex, one parameter family of flat connections called the A-model or Dubrovin connections. Let ~ denote the parameter. Associated to them is the quantum D module D/I over the Heisenberg algebra of first order differential operators on a complex torus. An element of I gives a relation in the quantum cohomology of M by taking the limit...

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Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated étale (φ,Γ)-module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarily étale (φ,Γ)-modules over the Robba ring, of the Euler-Poincaré characteristic formula and Tate local duality for p-adic represent...

For Y a closed normal subvariety of codimension c of a smooth C–variety X, Brylinski and Kashiwara showed in [BK81] that the local cohomology module HcY (X,OX) contains a unique simple DX– submodule, denoted by L(Y, X). In this paper the analogous result is shown for X and Y defined over a perfect field of finite characteristic. Moreover, a local construction of L(Y,X) is given, relating it to ...

The cohomology of a Hopf algebroid related to the Adams-Novikov spectral sequence for formal ,4-modules is studied in the special case in which A is the ring of integers in the field obtained by adjoining pth roots of unity to Qp , the p-adic numbers. Information about these cohomology groups is used to give new proofs of results about the E2 term of the Adams spectral sequence based on 2-local...

Let R = ⊕ n≥0 Rn be a Noetherian homogeneous ring with onedimensional local base ring (R0,m0). Let q0 ⊆ R0 be an m0-primary ideal, let M be a finitely generated graded R-module and let i ∈ N0. Let Hi R+ (M) denote the i-th local cohomology module of M with respect to the irrelevant ideal R+ := ⊕ n>0 Rn of R. We show that the first Hilbert-Samuel coefficient e1 ( q0, Hi R+ (M)n ) of the n-th gra...

A cohomological support, Supp A (M), is defined for finitely generated modules M over a left noetherian ring R, with respect to a ring A of central cohomology operations on the derived category of R-modules. It is proved that if the A-module Ext R (M, M) is noetherian and Ext R (M, R) = 0 for i ≫ 0, then every closed subset of Supp A (M) is the support of some finitely generated R-module. This ...

Group algebras are Hopf algebras, and their Hopf structure plays crucial roles in representation theory and cohomology of groups. A Hopf algebra is an algebra A (say over a field k) that has a comultiplication (∆ : A → A ⊗k A) generalizing the diagonal map on group elements, an augmentation (ε : A → k) generalizing the augmentation on a group algebra, and an antipode (S : A → A) generalizing th...

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...