Bases of associated Galois modules in general wildly ramified extensions and in elementary abelian extensions of degree p²

2025/11/25 by Bondarko, Mikhail V., Ladny, Kirill S., Pimenov, Konstantin I.
#11S20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.20634

Abstract

For a wildly ramified extension K/k of complete discrete valuation fields we study collections of elements of k[G] (where G=Gal(K/k)) that fit well for constructing bases of various associated Galois modules and orders. In the case G=(Z/pZ)² (where p is the characteristic of residue fields) we are able to compute the action of the elements (σ₁-1)ⁱ(σ₂-1)^j, 0≤ i,j≤ p-1, on the valuation filtration; here σ₁,σ₂ are generators of G. If the ramification jumps of K/k are distinct modulo p² then these elements do yield "good enough" bases in question.

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