Derived Hecke action at p and the ordinary p-adic cohomology of arithmetic manifolds

2020/04/14 by Khare, Chandrashekhar, Ronchetti, Niccolò
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2004.06241

Abstract

We study the derived Hecke action at p on the ordinary p-adic cohomology of arithmetic subgroups of semisimple groups \mathrm G(\mathbb Q), i.e., we study the derived version of Hida's theory for ordinary Hecke algebras. This is the analog at ℓ=p of derived Hecke actions studied by Venkatesh in the tame case. We show that properties of the derived Hecke action at p are related to deep conjectures in Galois cohomology which are higher analogs of the classical Leopoldt conjecture.

Related

• Non-vanishing mod p of derived Hecke algebra of the multiplicative group over number field
• Derived Hecke action on the trivial cohomology of division algebras
• Potential automorphy and the Leopoldt conjecture
• Towards the p-adic derived Hecke algebra for weight one forms
• A note on some p-adic analytic Hecke actions