Two contributions to the arithmetic of varieties : R-equivalence and unramified cohomology
type: Dataset
contact point: Organization
  fn: CCSD
keyword: chow-groups
keyword: theses
keyword: unramified-cohomology
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: groupes-de-chow
keyword: rationally-connected-varieties
keyword: varietes-rationnellement-connexes
keyword: r-equivalence
keyword: cohomologie-non-ramifiee
landing page: https://theses.hal.science/tel-00769925
description: In this Ph.D. thesis, we investigate some arithmetic properties of algebraic varieties. The thesis consists of two parts, divided into eight chapters. The first part is devoted to the study of R-equivalence on rational points of algebraic varieties. In chapter I.1, we prove that for some families X→Y of smooth projective geometrically rational varieties defined over a finite extension of Qp, the number of R-equivalence classes on Xy(k) is a locally constant function on Y(k). In chapter I.2, we establish the triviality of R-equivalence for rationally simply connected varieties defined over C(t). In chapter I.3, we introduce and analyze a different equivalence relation on rational points of varieties defined over a field equipped with a discrete valuation, and then compare it with R-equivalence. In chapter I.4, we study R-equivalence for varieties over real closed and p-adically closed fields. The second part of the thesis deals with some questions involving unramified cohomology. In chapter II.1, we use the third unramified cohomology group to give an example of a smooth, projective, geometrically rational variety X defined over a finite field Fp, such that the map from the Chow group of codimension two cycles on X to the Chow group of codimension two cycles over an algebraic closure, fixed by the Galois action, is not surjective. In chapter II.2, we prove the vanishing of the third unramified cohomology group for certain fibrations over a surface defined over a finite field whose generic fibre is a Severi-Brauer variety. In chapter II.3, we show that certain terms of the Bloch-Ogus spectral sequence are birational invariants for varieties over fields of bounded cohomological dimension. Then in the case of a finite field, we relate one of these invariants to the cokernel of the l-adic cycle class map for 1-cycles. Finally, in chapter II.4, we establish a “bound” for ramification of elements of the group Hr(K, Z/n), r>0, where K is the function field of an integral va…
identifier: NNT: 2011PA112197
issued: 2026-05-28T21:48:11.080041
language: fr
modified: 2026-05-28T21:48:11.080048

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type: Agent

Two contributions to the arithmetic of varieties : R-equivalence and unramified cohomology
type: Distribution
access URL: https://theses.hal.science/tel-00769925
format: HTML
issued: 2026-05-28T21:48:11.113433
modified: 2026-05-28T21:48:11.047495