Speaker
Description
Let F be a field of characteristic 2. The Kato-Milne cohomology group of F of degree m is denoted by H_2^{m+1}(F). This is an important group for the study of quadratic forms in characteristic 2 as was shown in a celebrated result due to Kato. Our aim in this talk is to give a complete description of the group H_2^{m+1}(F(t)) of the rational function field F(t). This will be done in terms of thegroup H_2^{m+1}(F) and some residue groups corresponding to simple finite extensions of F. As an application, we prove that the kernel of the homomorphism H_2^{m+1}(F) − −− > H_2^{m+1}(F(p)), induced by scalar extension, coincides with the annihilator of the logarithmic differential form dp/p, where F(p) is the function field of the affine hypersurface given by an arbitrary irreducible and normed polynomial p. This talk is a part of my PhD thesis supervised by Ahmed Laghribi (LML, Universit´e d’Artois).