A remark on Ext groups for motives with maximal unipotent radicals

2025/06/19 by Eskandari, Payman
Mathematics · #11G99 #14C15 #18M25 #19E15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.16540

openalex publication_date 2025/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T be a neutral tannakian category over a field of characteristic 0. Let M be an object of T with a filtration 0=F₀M\subsetneq F₁M\subsetneq ⋯\subsetneq F_kM=M, such that each successive quotient F_iM/F_i-1M is semisimple. Assume that the unipotent radical of the tannakian fundamental group of M is as large as it is permitted under the constraints imposed by the filtration (F_\bullet M). In this note, we first describe the Ext¹ groups in the tannakian subcategory of T generated by M. We then give two applications for motives, one involving 1-motives and another involving mixed Tate motives, leading to some implications of Grothendieck's period conjecture.

Citations

• Depth one part of Tannakian groups of filtrations
• Tannakian fundamental groups of blended extensions
• On blended extensions in filtered abelian categories and motives with maximal unipotent radicals
• Hecke Actions on Loops and Periods of Iterated Shimura Integrals
• A note on 1-motives
• Mixed Tate motives and the unit equation
• On the Mumford-Tate conjecture for 1-motives

Related

• Tannakian fundamental groups of blended extensions
• Depth one part of Tannakian groups of filtrations
• Tate motives and the fundamental group
• Groupes fondamentaux motiviques de Tate mixte
• On blended extensions in filtered abelian categories and motives with maximal unipotent radicals