Visiting addressNiels Henrik Abels hus Moltke Moes vei 35 (map)
In this talk, we will present a relation between the classical Chow group of relative 0-cycles on a regular scheme X, projective and flat over an excellent Henselian discrete valuation ring A with perfect residue field k, and the so-called cohomological Chow group of zero cycles of the special fiber. If k algebraically closed and with finite coefficients (prime to the residue characteristic) these groups turn out to be isomorphic. This generalizes a previous argument due to Esnault-Kerz-Wittenberg to the case of regular models with arbitrary reduction. From this, one can re-prove in case of bad reduction that the étale cycle class map for relative 0-cycles with finite coefficients on X is an isomorphism, a result due to Saito and Sato in the case of semi-stable reduction. This is a joint work with Amalendu Krishna.
Grothendieck invented the category of numerical motives. From this, the abelian category of pure motives can be obtained assuming his conjectures. This category serves as a universal cohomology theory for schemes smooth and projective over a field. It is expected that there is an abelian category of mixed motives, which contains the abelian category of pure motives as a full subcategory and serves as a universal cohomology theory for schemes smooth but not necessarily projective over a field. I will explain how mixed motives looks assuming several conjectures, and I will give some unconditional examples including 2-motives.
Recently two different refinements of Voevodsky's theory of presheaves with transfers were introduced: the first one is the theory of framed presheaves based on the unpublished notes by Voevodsky and developed by Garkusha and Panin and the second one is the theory of Milnor-Witt presheaves due to Calmes and Fasel. I will review some relations between these theories and explain that the hearts of the homotopy t-structures on the corresponding categories of motives are naturally equivalent. The talk is based on a joint work with A. Neshitov.
Paul Arne Østvær will hold a seminar at the University of Osnabrück.
Glen Wilson will hold a seminar at the Oberseminar Topologie at the University of Osnabrück.
Glen Wilson will hold a seminar at the Wuppertal Topology Seminar.
Paul Arne Østvær will hold a seminar at the Oberseminar Algebra, Geometrie und Zahlentheorie at the University of Duisburg-Essen.
Paul Arne Øsvær will talk about A1-contractible varieties in the Oberseminar on Arithmetische und Algebraische Geometrie, at the Mathematisches Institut der Universität München.
Glen Wilson will hold an electronic seminar at the Electronic Computational Homotopy Theory Seminar run by Dan Isaksen.
Glen Wilson will give a talk in the UiO Topology Seminar.
Paul Arne Østvær spoke at the workshop Etale and Motivic Homotopy Theory 2017 at the University of Heidelberg.
Glen Wilson will give a seminar at NTNU in the Topology Seminar.
Paul Arne Østvær will speak at the conference Algebraic K-Theory and Arithmetic at the Polish Academy of Sciences in Będlewo.