Computability of the étale Euler-Poincaré characteristic

Jin, J. (2017)

Doctoral Thesis

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.

 

• Computational arithmetic geometry
• étale cohomology

• All authors: Jin, J.
• Supervisor: Edixhoven, S.J.; Taelman, L.D.J.
• Committee: Diem, C.; Lenstra, H.W.; Orgogozo, F.; Smit, B. de; Vaart, A.W. van der
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematical Institute, Science, Leiden University
• Date: 2017-01-18