On anticyclotomic Euler and Kolyvagin systems

2025/05/13 by Luca Mastella, Francesco Zerman, Mastella, Luca +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Class (philosophy) #Euler system #Euler's formula #Modular design #Representation (politics) #math.NT

paper · pdf · doi:10.1007/s40316-026-00269-y

published in Annales mathématiques du Québec (Springer Science+Business Media)

openalex publication_date 2026/07/20 · openalex created_date 2026/07/21 · openalex updated_date 2026/08/05

Abstract

We introduce an axiomatization of the notion of ( p-complete) anticyclotomic Euler system for a wide class of Galois representations, including those attached to a cuspidal eigenform and to a Hida family of modular forms. Under a minimal set of assumptions, we show how to build from these data a universal Kolyvagin system for the representation and for its anticyclotomic twist. Eventually, we recover some applications to the structure of Selmer groups and Iwasawa main conjectures and we review a few concrete examples of these abstract notions that can be found in the literature.

Citations

• Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms
• The Heegner point Kolyvagin system
• On ordinary ?-adic representations associated to modular forms
• Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques

Cited by

• Quaternionic Kolyvagin systems and Iwasawa theory for Hida families

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