Homological transcendence degree

• Autores: Amnon Yekutieli, James J. Zhang
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 93, Nº 1, 2006, págs. 105-137
• Idioma: inglés
• DOI: 10.1017/s0024611505015698
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let $D$ be a division algebra over a base field $k$. The homological transcendence degree of $D$, denoted by $\text{Htr}\; D$, is defined to be the injective dimension of the algebra $D \otimes_k D^{\circ}$. We show that $\text{Htr}$ has several useful properties which the classical transcendence degree has. We extend some results of Resco, Rosenberg, Schofield and Stafford, and compute $\text{Htr}$ for several classes of division algebras. The main tool for the computation is Van den Bergh's rigid dualizing complex.