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東工大数論・幾何学セミナー： Andrew Macpherson 氏

講演タイトル: A Tannakian perspective on rigid analytic geometry
アブストラクト: 　Raynaud's conception of analytic geometry contends that the category of analytic spaces over a non-Archimedean field is a (suitably "geometric") localisation of the category of formal schemes over the ring of integers at a class of modifications "along the central fibre". Unfortunately, as with all existing presentations of non-Archimedean geometry, this viewpoint is confounded by a proliferation of technical difficulties if one does not impose absolute finiteness conditions on the formal schemes under consideration.
　I will argue that by combining Raynaud's idea with a Tannakian perspective which prioritises the module category, we can obtain a reasonable framework for rigid analytic geometry with no absolute finiteness hypotheses whatsoever, but which has descent for finitely presented modules.

更新日：2020.01.08