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arXiv · 2306.13180

Non-surjective Milnor patching diagrams

Alexandr Grebennikov
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Abstract

Milnor patching diagram is essentially the commutative square of rings, over which gluing of finitely generated projective modules is possible in the strongest sense. Necessary and sufficient conditions for a square to be Milnor patching diagram were studied by Milnor, Beauville-Laszlo and Landsburg. We relate this question to determinant-induced factorization in matrix rings to construct a series of non-surjective Milnor patching diagrams, settling the question of Landsburg, and make a step towards the classification of such examples. Also we consider a possible generalization of the notion of Milnor patching diagram to arbitrary subcategories of modules and obtain a classification result for this setting.

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Alexandr Grebennikov. 2023-06-19. Non-surjective Milnor patching diagrams. https://arxiv.org/abs/2306.13180

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