Cohomology and graded Witt group kernels for extensions of degree four in characteristic two

Witt Kernels of Quadratic Forms for Multiquadratic Extensions in Characteristic 2

Let F be a field of characteristic 2 and let K/F be a purely inseparable extension of exponent 1. We show that the extension is excellent for quadratic forms. Using the excellence we recover and extend results by Aravire and Laghribi who computed generators for the kernel Wq(K/F ) of the natural restriction map Wq(F ) → Wq(K) between the Witt groups of quadratic forms of F and K, respectively, ...

Cohomology of Split Group Extensions and Characteristic Classes

There are characteristic classes that are the obstructions to the vanishing of the differentials in the Lyndon-Hochischild-Serre spectral sequence of an extension of an integral lattice L by a group G. These characteristic classes exist in the r-th page of the spectral sequence provided differentials di = 0 for all i < r. If L further decomposes into a sum of G-sublattice L = L ⊕ L, we show tha...

Cohomology of Group Extensions

Introduction. Let G be a group, K an invariant subgroup of G. The purpose of this paper is to investigate the relations between the cohomology groups of G, K, and G/K. As in the case of fibre spaces, it turns out that such relations can be expressed by a spectral sequence whose term E2 is HiG/K, HiK)) and whose term Em is the graduated group associated with i7(G). This problem was first studied...

Cohomology of the Siegel modular group of degree two and level four

We compute the cohomology of the subgroup of the integral symplectic group of degree 2 consisting of matrices γ ≡ 1 mod 4. This is done by computing the cohomology of the moduli space of principally polarized abelian surfaces with a level 4 structure. This space has a projective smooth compactification whose topology was analyzed by Lee and Weintraub in a recent work.

The Galois Cohomology of Square-Classes of Units in Klein-Four Group Extensions of Characteristic Not Two: A Thesis Submitted to the Department of Mathematics for Honors