2018/04/30 by Gebhard Boeckle, David-A. Guiraud, Boeckle, Gebhard +5
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #11R32 #11R34 #11Y40 #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1805.00131
openalex publication_date 2018/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider questions in Galois cohomology which arise by considering mod p Galois representations arising from automorphic forms. We consider a Galois cohomological analog for the standard heuristics about the distribution of Wieferich primes, i.e. prime p such that 2p-1 is 1 mod p2. Our analog relates to asking if in a compatible system of Galois representations, for almost all primes p, the residual mod p representation arising from it has unobstructed deformation theory. This analog leads in particular to formulating a mod p analog for almost all primes p of the classical Leopoldt conjecture, which has been considered previously by G. Gras. Leopoldt conjectured that for a number field F, and a prime p, the p-adic regulator RF,p is non-zero. The mod p analog is that for a fixed number field F, for almost all primes p, the p-adic regulator RF,p is a unit at p.