A Complete Description of the Cohomological Invariants of Even Genus Hyperelliptic Curves

When the genus g is even, we extend the computation of mod 2 cohomological invariants of ℋgto non algebraically closed fields, we give an explicit functorial description of the invariants and we completely describe their multiplicative structure. In the Appendix, we show that the cohomological invariants of the compactification (Formula presented)gare trivial, and use our methods to give a very short proof of a result by Cornalba on the Picard group of the compactification (Formula presented)gand extend it to positive characteristic.