The spin of prime ideals and level-raising of even Galois representations

2025/12/16 by Fischer, Marius, Uttenthal, Peter Vang
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2512.14901

openalex publication_date 2025/12/16 · openalex created_date 2025/12/19 · openalex updated_date 2026/07/28

Abstract

By extending the notion of spin of prime ideals, we show that a short character sum conjecture implies that the set of primes raising the level of a certain even Galois representation has density 2/3, as conjectured by Ramakrishna in 1998.

Citations

• Elliptic curves and spin
• Weak approximation on the norm one torus
• Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations
• The geometric sieve and the density of squarefree values of invariant polynomials
• The spin of prime ideals
• Transcendental l-adic Galois representations
• Constructing semisimple p-adic Galois representations with prescribed properties

Related

• Constructing semisimple p-adic Galois representations with prescribed properties
• Level-raising of even representations of tetrahedral type and equidistribution of lines in the projective plane
• The spin of prime ideals
• The density of ramified primes in semisimple p-adic Galois representations
• A level raising result for modular Galois representations modulo prime powers