A vanishing theorem for oriented intersection multiplicities

• Autores: Jean Fasel, V. Srinivas
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 2-3, 2008, págs. 447-458
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n3.a5
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let $A$ be a regular local ring containing $1/2$, which is either equicharacteristic, or is smooth over a d.v.r. of mixed characteristic. We prove that the product maps on derived Grothendieck-Witt groups of $A$ satisfy the following property: given two elements with supports which do not intersect properly, their product vanishes. This gives an analogue for ``oriented intersection multiplicities'' of Serre's vanishing result for intersection multiplicities. It also suggests a Vanishing Conjecture for arbitrary regular local rings containing $1/2$, which is analogous to Serre's (which was proved independently by Roberts, and Gillet and Soul\'e).