Galois coinvariants of the unramified Iwasawa modules of multiple $$\mathbb {Z}_p$$-extensions

Unramified Abelian Extensions of Galois Covers

We consider a ramified Galois cover φ : X̂ → Px of the Riemann sphere Px, with monodromy group G. The monodromy group over Px of the maximal unramified abelian exponent n cover of X̂ is an extension nG̃ of G by the group (Z/nZ), where g is the genus of X̂. Denote the set of linear equivalence classes of divisors of degree k on X̂ by Pic(X̂) = Pic. This is equipped with a natural G action. We show tha...

Asymptotics of coinvariants of Iwasawa modules under non-normal subgroups

Let G be a pro-p p-adic analytic group, thought of as a closed subgroup of GLN (Zp), and let Σ be a closed subgroup of G. Write Λ for the completed group algebra Zp[[G]] and let M be a finitely generated Λ-module. Let G = G ⊃ G ⊃ G ⊃ . . . be the descending sequence of principal congruence subgroups of G; write Gn for the quotient G/G and Σn for the image of Σ in Gn. Write Mn for the coinvarian...

CONSTRUCTION OF MAXIMAL UNRAMIFIED p-EXTENSIONS WITH PRESCRIBED GALOIS GROUPS

For any number field F (not necessary of finite degree) and prime number p, let Lp(F ) denote the maximal unramified p-extension over F , and put G̃F (p) = Gal(Lp(F )/F ). Though the structure of G̃F (p) has been one of the most fascinating theme of number theory, our knowledge on it is not enough even at present: It had been a cerebrated open problem for a long time whether G̃F (p) can be infinit...

Galois modules, Iwasawa theory and leading term conjectures

extensions of some polynomial inequalities to the polar derivative

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