Koszul complexes and symmetric forms over the punctured affine space

• Autores: Paul Balmer, Stefan Gille
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 91, Nº 2, 2005, págs. 273-299
• Idioma: inglés
• DOI: 10.1112/s0024611504015199
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let $X$ be a regular separated scheme of finite Krull dimension and let $U^{n}_{X} \subset A^{n}_{X}$ be the punctured affine $n$-space over $X$. We show that the total graded Witt ring of $U^{n}_{X}$ is a free graded module over the total graded Witt ring of $X$ with two generators $1$ and $\epsilon$. The second generator satisfies the equation $\epsilon^{2} = 1$ when $n = 1$ and $\epsilon^{2} = 0$ when $n \geq 2$.