Universiteit Leiden

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Dissertation

Computability of the étale Euler-Poincaré characteristic

Promotor: S.J. Edixhoven, L.D.J. Taelman

Author
J. Jin
Date
18 January 2017
Links
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.

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