Related papers: Mild pro-p groups and the Koszulity conjectures

Let $E/\mathbb{Q}$ be an elliptic curve, $p$ a prime and $K_{\infty}/K$ the anticyclotomic $\mathbb{Z}_p$-extension of a quadratic imaginary field $K$ satisfying the Heegner hypothesis. In this paper we make a conjecture about the fine…

Let $p$ be a prime and $\mathbb{F}_p$ be a finite field of $p$ elements. Let $\mathbb{F}_pG$ denote the group algebra of the finite $p$-group $G$ over the field $\mathbb{F}_p$ and $V(\mathbb{F}_pG)$ denote the group of normalized units in…

We investigate some properties of the $p$-elements of a profinite group $G$. We prove that if $p$ is odd and the probability that a randomly chosen element of $G$ is a $p$-element is positive, then $G$ contains an open prosolvable subgroup.…

Suppose $R$ is a profinite ring. We construct a large class of profinite groups $\widehat{{\scriptstyle\bf L}'{\scriptstyle\bf H}_R}\mathfrak{F}$, including all soluble profinite groups and profinite groups of finite cohomological dimension…

Let p be a prime and F a field containing a primitive pth root of unity. Then for n in N, the cohomological dimension of the maximal pro-p-quotient G of the absolute Galois group of F is <=n if and only if the corestriction maps H^n(H,Fp)…

For prime power $q=p^d$ and a field $F$ containing a root of unity of order $q$ we show that the Galois cohomology ring $H^*(G_F,\dbZ/q)$ is determined by a quotient $G_F^{[3]}$ of the absolute Galois group $G_F$ related to its descending…

Let $N$ and $p$ be prime numbers $\geq 5$ such that $p$ divides $N-1$. Let $I$ be Mazur's Eisenstein ideal of level $N$ and $H_+$ be the plus part of $H_1(X_0(N), \mathbf{Z}_p)$ for the complex conjugation. We give a conjectural explicit…

We call a pro-$p$ group $G$ Frattini-injective if distinct finitely generated subgroups of $G$ have distinct Frattinis. This paper is an initial effort toward a systematic study of Frattini-injective pro-$p$ groups (and several other…

We present several constraints on the absolute Galois groups G_F of fields F containing a primitive pth root of unity, using restrictions on the cohomology of index p normal subgroups from a previous paper by three of the authors. We first…

We classify the finite groups with the property that any two different character codegrees are coprime. In general, we conjecture that if $k$ is a positive integer such that for any prime $p$ the number of character codegrees of a finite…

For a prime number $p$ and a free pro-$p$ group $G$ on a totally ordered basis $X$, we consider closed normal subgroups $G^\Phi$ of $G$ which are generated by $p$-powers of iterated commutators associated with Lyndon words in the alphabet…

Let $G$ be a finitely generated pro-$p$ group of positive rank gradient. Motivated by the study of Hausdorff dimension, we show that finitely generated closed subgroups $H$ of infinite index in $G$ never contain any infinite subgroups $K$…

Let p be an odd prime satisfying Vandiver's conjecture. We consider two objects, the Galois group X of the maximal unramified abelian pro-p extension of the compositum of all Z_p-extensions of the pth cyclotomic field and the Galois group G…

K. Hess's theory of homotopical descent, applied to the large categories of motives defined recently by Blumberg, Gepner, and Tabuada, suggests that the Koszul dual of Waldhausen's K-theory of the sphere spectrum, regarded as a supplemented…

Let $p$ be a prime, $k$ a finite extension of $\mathbf{F}_p$ of cardinal $q$, $l$ a finite extension of $k$ of group $\Sigma=\mathrm{Gal}(l|k)$, and $T$ a subgroup of $l^\times$. Using the method of "little groups", we classify irreducible…

In this paper we prove that if G is a connected, simply-connected, semi-simple algebraic group over an algebraically closed field of sufficiently large characteristic, then all the blocks of the restricted enveloping algebra (Ug)_0 of the…

This paper considers Weyl modules for a simple, simply connected algebraic group over an algebraically closed field $k$ of positive characteristic $p\not=2$. The main result proves, if $p\geq 2h-2$ (where $h$ is the Coxeter number) and if…

Let p be prime, k a finite field of characteristic p, and G a virtually pro-p group. We prove an analogue of the Green Correspondence for finitely generated modules over the completed group algebra k[[G]].

For a prime number $\ell$ we say that an oriented pro-$\ell$ group $(G,\theta)$ has the Bogomolov-Positselski property if the kernel of the canonical projection on its maximal $\theta$-abelian quotient $\pi^{ab}_{G,\theta}\colon G\to…

In this paper we compute the Galois cohomology of the pro-p completion of primitive link groups. Here, a primitive link group is the fundamental group of a tame link in the 3-sphere whose linking number diagram is irreducible modulo p (e.g.…