Recent zbMATH articles in MSC 14F35https://www.zbmath.org/atom/cc/14F352021-03-30T15:24:00+00:00WerkzeugSmooth affine model for the framed correspondences spectrum.https://www.zbmath.org/1455.140412021-03-30T15:24:00+00:00"Druzhinin, A."https://www.zbmath.org/authors/?q=ai:druzhinin.andrei-eSummary: Morel-Voevodsky's unstable pointed motivic homotopy category \(\mathbf{H}_{\bullet}(k)\) over an infinite perfect field is considered. For a smooth affine scheme \(Y\) over \(k\), a smooth ind-scheme \(F_l(Y)\) and an open subscheme \(E_l(Y)\) are constructed for all \(l > 0\), so that the motivic space \(F_l(Y)/E_l(Y)\) is equivalent in \(\mathbf{H}_{\bullet}(k)\) to the motivic space \({\Omega}_{{\mathbb{P}}^1}^{\infty}\sum \limits_{\mathbb{P}^1}^{\infty}\left(Y\times{T}^l\right)\), \(T=\left(\mathbb{A}^1/\mathbb{A}^1-0\right)\), \(l>0 \). The construction is not functorial on the category of affine schemes but is functorial on the category of so-called framed schemes constructed for this purpose.Anabelian geometry of curves over algebraically closed fields of positive characteristic: the case of one-punctured elliptic curves.https://www.zbmath.org/1455.140612021-03-30T15:24:00+00:00"Sarashina, Akira"https://www.zbmath.org/authors/?q=ai:sarashina.akiraSummary: This article is an announcement of the author's recent work on anabelian geometry over algebraically closed fields of positive characteristic. We review some known results in this area and give a sketch of the proof of the main result which concerns reconstruction of curves of \((1,1)\)-type by their geometric fundamental groups.