Custom cover image
Custom cover image

Decomposition of the diagonal, intermediate Jacobians, and universal codimension-2 cycles in positive characteristic = Décomposition de la diagonale, jacobiennes intermédiaires, et cycles universels de codimension 2 en caractéristique positive / J. D. Achter, S. Casalaina & C. Vial

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Summary language: French, English Series: Astérisque ; 455 (2025)Publisher: Paris : Société Mathématique de France, [2025]Description: xxi, 115 SeitenISBN:
  • 9782379052002
Other title:
  • Décomposition de la diagonale, jacobiennes intermédiaires, et cycles universels de codimension 2 en caractéristique positive
Subject(s): Additional physical formats: No title | Erscheint auch als: Decomposition of the diagonal, intermediate Jacobians, and universal codimension-2 cycles in positive characteristic. Online-Ausgabe Paris : Société Mathématique de France, 2025. 1 Online-Ressource (xxi, 115 Seiten)MSC: MSC: 14C25 | 14E08 | 14F20 | 14G17 | 14K30 | 14J30 | 14M20RVK: RVK: SI 832LOC classification:
  • QA402.2
Summary: We consider the connections among algebraic cycles, Abelian varieties, and stable rationality of smooth projective varieties in positive characteristic. Recently Voisin constructed two new obstructions to stable rationality for rationally connected complex projective threefolds by giving necessary and sufficient conditions for the existence of a cohomological decomposition of the diagonal. In this paper, we show how to extend these obstructions to rationally chain connected threefolds in positive characteristic via ℓ-adic cohomological decomposition of the diagonal. This requires extending results in Hodge theory regarding intermediate Jacobians and Abel-Jacobi maps to the setting of algebraic representatives. For instance, we show that the algebraic representative for codimension-two cycle classes on a geometrically stably rational threefold admits a canonical auto-duality, which in characteristic zero agrees with the principal polarization on the intermediate Jacobian coming from Hodge theory. As an application, we extend a result of Voisin, and show that in characteristic greater than two, a desingularization of a very general quartic double solid with seven nodes does not admit a universal codimension-two cycle class. In the process, we establish some results on the moduli space of nodal degree-four polarized K3 surfaces in positive characteristic.Summary: "Nous considérons les liens entre les cycles algébriques, les variétés abéliennes et la rationalité stable des variétés projectives lisses en caractéristique positive. Voisin a construit deux nouvelles obstructions à la rationalité stable pour les solides projectifs lisses complexes rationnellement connexes en donnant des conditions nécessaires et suffisantes pour l'existence d'une décomposition cohomologique de la diagonale. Nous étendons ces obstructions à la caractéristique positive, via la décomposition cohomologique l-adique de la diagonale, en transférant des résultats en théorie de Hodge concernant les jacobiennes intermédiaires (et leur autodualité) et les applications d'Abel-Jacobi au cadre des représentants algébriques."-- Back coverPPN: PPN: 1919251928
Holdings
Item type Home library Shelving location Call number Status Barcode
Freihandbestand ausleihbar Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 533-455.2025 Available 36543160090
Total holds: 0

Zusammenfassung in französischer und englischer Sprache

KIT – The Research University in the Helmholtz Association                         Home | Impressum | Datenschutz | Barrierefreiheit | KIT