4 problems

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The non-abelian zeta-distribution main conjecture for Artin motives
Zeta-distribution main conjecture. There exist $f,g\in\Lambda$ such that $(\operatorname{rn}(f_ng_n^{-1}))_n$ is the zeta distribution $\mathcal{L}_S(G_\infty,M^\lor,1-k)$ and the…
Conjectureopenartin-motives iwasawa-theory noncommutative-algebraarXiv posted 2 days ago
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Damerell–Longo–Rotger modular description of the adjoint cohomology space
Let $f$ be the modular form in the paper, let $\varrho_f$ be its associated Galois representation, and let $\operatorname{ad}^0\varrho_f$ denote its trace-zero adjoint representati…
Conjecturesolvedartin-motives galois-representations overconvergent-modular-formsarXiv posted 2 days ago
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Weak $p$ -adic Schanuel conjecture for anti-cyclotomic $\mathscr{L}$ -invariants
Let $\varphi$ be a character as in the paper, with conjugate character $\bar\varphi$ , and let $\mathscr{L}_{\text{-}}(\varphi)$ and $\mathscr{L}_{\text{-}}(\bar\varphi)$ denote the…
Conjecturesolvedartin-motives number-theory p-adic-l-functionsarXiv posted 2 days ago
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The Artin-motive conjecture for motives with trivial Hodge numbers
Let $M$ be a pure $\mathbb Q$ -motive over a number field $F$ , and let $M_{\operatorname{dR}}$ be its de Rham realization with Hodge filtration. Artin-motive conjecture. If … then…
Conjecturesolvedartin-motives motivesarXiv posted 2 days ago

The non-abelian zeta-distribution main conjecture for Artin motives