Let k be a field of characteristic p>0 and let H finite group or scheme. We show that the negative Tate cohomology ring Hˆ?0(H,k) can realized as endomorphism trivial module in Verdier localization stable category kG-modules for G an extension H. This means some cases is local with infinitely generated radical square zero. stands stark contrast to known calculations which degree zero component ...

In this article we prove conditions under which a certain parabolic group cohomology space over a finite field F is a faithful module for the Hecke algebra of Katz modular forms over an algebraic closure of F. These results can e.g. be used to compute Katz modular forms of weight one with methods of linear algebra over F. MSC Classification: 11F25 (primary), 11F33, 11F67, 11Y40 (secondary).

Let X be a space and write LX for its free loop space equipped with the action of the circle group T given by dilation. We compute the equivariant cohomology H(LXhT;Z/p) as a module over H ∗(BT;Z/p) when X = CP for any positive integer r and any prime number p. The computation implies that the associated mod p Serre spectral sequence collapses from the E3-page. MSC: 55N91; 58E05; 55P35; 18G50

INTRODUCTION. If X is a CW complex with cells only in even dimensions and R is a ring, then, by an elementary result in cellular cohomology theory, the ordinary eohomology H*(X;R) of X with R coefficients is a free, 7/-graded R-module. Since this result is quite useful in the study of well-behaved complex manifolds like projective spaces or Grassmannians, it would be nice to be able to generali...

We define the cohomological Burnside ring B(G,M) of a finite group G with coefficients in a ZG-module M as the Grothendieck ring of the isomorphism classes of pairs [X, u] where X is a G-set and u is a cohomology class in a cohomology group H X(G,M). The cohomology groups H ∗ X(G,M) are defined in such a way that H∗ X(G, M) ∼= ⊕iH∗(Hi,M) when X is the disjoint union of transitive G-sets G/Hi. I...

In the previous paper [17], the author defined equivariant Floer cohomology for a complete intersection in a toric variety and showed that it is isomorphic to the small quantum D-module after a mirror transformation when the first Chern class c1(M) of the tangent bundle is nef. In this paper, even when c1(M) is not nef, we show that the equivariant Floer cohomology reconstructs the big quantum ...

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over Q, and let Γ ⊂ G be a appropriate neat arithmetic subgroup. We present two algorithms to compute the action of the Hecke operators on H(Γ;Z) for all i. This simultaneously generalizes the modular symbol algorithm of Ash-Rudolph [7] to a larger class of groups, and provides techniques to compute the H...

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over Q, and let Γ ⊂ G be a appropriate neat arithmetic subgroup. We present two algorithms to compute the action of the Hecke operators on H(Γ;Z) for all i. This simultaneously generalizes the modular symbol algorithm of Ash-Rudolph [7] to a larger class of groups, and provides techniques to compute the H...

For a coherent filtered D-module we show that the dual of each graded piece over the structure sheaf is isomorphic to a certain graded piece of the ring-theoretic local cohomology complex of the graded quotient of the dual of the filtered D-module along the zero-section of the cotangent bundle. This follows from a similar assertion for coherent graded modules over a polynomial algebra over the ...