The abelian fundamental group with modulus in mixed characteristic

2025/10/23 by Ooe, Ryosuke
#11S15 #14H30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.20138

Abstract

We define the abelian fundamental group with modulus of a regular flat scheme over a discrete valuation ring, taking into account wild ramification along a divisor. Our definition provides a mixed-characteristic analogue of the abelian fundamental group with modulus introduced by Kerz--Saito for smooth schemes over a perfect field. In this setting, we prove a Lefschetz-type theorem for strictly semi-stable schemes: restriction to a hypersurface of sufficiently large degree relative to the ramification induces an isomorphism of the abelian fundamental groups.

Citations

• F-characteristic cycle of a rank one sheaf on an arithmetic surface
• Lefschetz theorems for tamely ramified coverings
• Ramification of local fields with imperfect residue fields

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• Potentially Good Reduction of Barsotti-Tate Groups
• Mod ℓ representations of arithmetic fundamental groups II (A conjecture of A.J. de Jong)
• Arithmetic Restrictions on Geometric Monodromy
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