代数派生范畴的光滑性

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2018-10-17 DOI:10.17323/1609-4514-2020-2-277-309

A. Elagin, V. Lunts, Olaf M. Schnurer

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引用次数: 10

摘要

我们证明了有限维代数上有限生成模的有界派生范畴在完全域上的光滑性，从而回答了Iyama的一个问题。更一般地说，我们证明了这一命题适用于中心有限且中心有限生成为代数的完美域上的任何代数。这些结果是从一般的充分的平滑准则推导出来的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Smoothness of Derived Categories of Algebras

We prove smoothness in the dg sense of the bounded derived category of finitely generated modules over any finite-dimensional algebra over a perfect field, hereby answering a question of Iyama. More generally, we prove this statement for any algebra over a perfect field that is finite over its center and whose center is finitely generated as an algebra. These results are deduced from a general sufficient criterion for smoothness.

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来源期刊

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.