Computability of the étale Euler-Poincaré characteristic
Promotor: S.J. Edixhoven, L.D.J. Taelman
- J. Jin
- 18 January 2017
- Thesis in Leiden Repository
In this dissertation, a primitive recursive algorithm is given for the computation of the étale Euler-Poincaré characteristic (which is the alternating sum of the étale cohomology groups in the Grothendieck group of Galois modules) with finite coefficients, and on arbitrary varieties over a field. For smooth curves, a primitive recursive algorithm is given for the computation of the étale cohomology groups themselves, using a geometric interpretation of the elements of the first etale cohomology. The general case is then reduced to the case of smooth curves by making the standard dévissage techniques explicit.