Bigraded equivariant cohomology of real quadrics

Bigraded Cohomology of Z/2-equivariant Grassmannians

Local cohomology modules of bigraded Rees algebras

Formulas are obtained in terms of complete reductions for the bigraded components of local cohomology modules of bigraded Rees algebras of 0-dimensional ideals in 2-dimensional Cohen-Macaulay local rings. As a consequence, cohomological expressions for the coefficients of the Bhattacharya polynomial of such ideals are obtained.

Unramified Cohomology of Quadrics, Iii

This paper is the third and last instalment of our project of computation of the low-degree unramified cohomology of quadrics. As in the previous papers [15] and [16], we denote by η X the map H(F,Q/Z(n− 1))→ H nr(F (X)/F,Q/Z(n− 1)) for a smooth, projective quadric X defined over a field F of characteristic 6= 2. Recall that in these papers we proved that Ker η X is generated by symbols for n ≤...

Unramified Cohomology of Quadrics, Ii

We compute the unramified cohomology of quadrics of dimension 4 in degree 4 over an arbitrary field of characteristic different from 2. We find that it is related to classical invariants of a more elementary nature, such as the group of spinor norms and the projective special orthogonal group modulo Manin’s R-equivalence.

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology