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arXiv 0801.05072008-01-03math.RT

关于挠自由三元组

On torsion torsionfree triples

Pedro Nicolas

备注：: Ph. D. thesis, 184 pages

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摘要：

本文研究了阿贝尔范畴和三角范畴中的挠挠自由（=TTF）三元组。（注意，在一个三角化范畴中的TTF三元组本质上是与这个三角化范畴的双射数据。特别地，我们完成了Jans关于一类模上可裂TTF三元组的刻画，证明了广义Smashing猜想的一个弱形式，利用微分分次（=dg）范畴的同调满态给出了k-范畴的导出范畴中所有TTF三元组的显式描述flat dg范畴，并发展了一种无界的方法来证明Koenig关于普通代数的右有界导出范畴的元素的定理。

英文摘要：

We study torsion torsionfree(=TTF) triples in abelian and triangulated categories. (Notice that TTF triples in a triangulated category are essentially in bijection with recollement data for this triangulated category.) In particular, we complete Jans' characterization of split TTF triples on a category of modules, prove a weak version of the Generalized Smashing Conjecture, use homological epimorphisms of differential graded(=dg) categories to give an explicite description of all the TTF triples in the derived category of a k-flat dg category and develope an unbounded approach to Koenig's theorem on recollements of right bounded derived categories of ordinary algebras.

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