Computability of the étale Euler-Poincaré characteristic

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Computability of the étale Euler-Poincaré characteristic

Type: Doctoral Thesis
Title: Computability of the étale Euler-Poincaré characteristic
Author: Jin, J.
Issue Date: 2017-01-18
Keywords: Computational arithmetic geometry
étale cohomology
Abstract: 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.
Promotor: Supervisor: S.J. Edixhoven, L.D.J. Taelman
Faculty: Science
University: Leiden
Handle: http://hdl.handle.net/1887/45208
 

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