xuewen guan

A Galois Group of Order 5^649: The Fourth Graded Layer Is Longitude-Blind

Let K = Q(ζ₅) and let G be the Galois group of the maximal pro-5 extension of K unramified outside the five places above 5 and 11. The preceding paper determined G/λ₄(G), of order 5¹³⁹, from four Koch relators and a fully named arithmetic Frobenius longitude. This note determines...

Galois Cohomology Does Not Truncate: Total Collapse of the Finite-Precision Herr Complex and the Exact Euler-Characteristic Barrier

Fix a prime p. The integral cyclotomic period ring truncates to the finite rings Λ_N,m = (Z/p^N)[T]/(T^m) with φ(T) = (1+T)^p − 1 and γ(T) = (1+T)^c − 1: this tower is the inevitable home of any attempt to compute local Galois cohomology by exact finite arithmetic on the integral...

A Galois Group of Order 5^649: The Fourth Graded Layer Is Longitude-Blind

Let K = Q(ζ₅) and let G be the Galois group of the maximal pro-5 extension of K unramified outside the five places above 5 and 11. The preceding paper determined G/λ₄(G), of order 5¹³⁹, from four Koch relators and a fully named arithmetic Frobenius longitude. This note determines...