Formal completion of a category along a subcategory

Details Formal completion of a category along a subcategory Formal completion of a category along a subcategory

2010-06-24

arxiv.org/abs/1006.4721v2

Mathematics

Algebraic Geometry

27 pages, minor corrections, a new Corollary 5.6 and references added

Scientific paper

Following an idea of Kontsevich, we introduce and study the notion of formal completion of a compactly generated (by a set of objects) enhanced triangulated category along a full thick essentially small triangulated subcategory. In particular, we prove (answering a question of Kontsevich) that using categorical formal completion, one can obtain ordinary formal completions of Noetherian schemes along closed subschemes. Moreover, we show that Beilinson-Parshin adeles can be also obtained using categorical formal completion.

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