Finite torsors on projective schemes defined over a discrete valuation ring

نویسندگان

چکیده

Given a Henselian and Japanese discrete valuation ring $A$ flat projective $A$-scheme $X$, we follow the approach of Biswas-dos Santos to introduce full subcategory coherent modules on $X$ which is then shown be Tannakian. We prove that, under normality generic fibre, associated affine group pro-finite in strong sense (so that its functions Mittag-Leffler $A$-module) it classifies finite torsors $Q\to X$. This establishes an analogy Nori's theory essentially fundamental group. In addition, compare our with ones recently developed by Mehta-Subramanian Antei-Emsalem-Gasbarri. Using comparison former, show any quasi-finite torsor X$ has reduction structure one.

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ژورنال

عنوان ژورنال: Algebraic geometry

سال: 2023

ISSN: ['2313-1691', '2214-2584']

DOI: https://doi.org/10.14231/ag-2023-001