Frobenius reciprocity, modular connections, lattice isomorphism theorem and abstract principal ideals

2025/02/09 by Amartya Goswami, Goswami, Amartya, Zurab Janelidze +2
Mathematics · #03G30 #06A06 #06C05 #08B05 #13A15 #18E13 #18G50 #20J99 #Category Theory (math.CT) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2502.06010

openalex publication_date 2025/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this short note is to fill a gap in the literature: Frobenius reciprocity in the theory of doctrines is closely related to modular connections in projective homological algebra and the notion of a principal element in abstract commutative ideal theory. These concepts are based on particular properties of Galois connections which play an important role also in the abstract study of group-like structures from the perspective of categorical/universal algebra; such role stems from a classical and basic result in group theory: the lattice isomorphism theorem.

Related

• Explicit reciprocity laws and Iwasawa theory for modular forms
• Lectures on the cohomology of reciprocity sheaves
• Reciprocity in the Langlands program since Fermat's Last Theorem
• Frobenius Splitting in Commutative Algebra
• Reciprocity law for compatible systems of abelian mod p Galois representations