Related papers: Canonical subgroups via Breuil-Kisin modules

We introduce a new partial resolution of crystalline spaces of Galois representations when the gaps in Hodge--Tate weights are smaller than $p$, with no bound on ramification. Furthermore, when $n =3$ in the case of minimal regular weight,…

We consider the canonical representation of the absolute Galois group of the rational numbers in the outer automorphism group of the pro-p completion of the fundamental group of the projective line minus 0,1, and infinity. Deligne has…

In this paper we study the universal lifting spaces of local Galois representations valued in arbitrary reductive group schemes when $\ell \neq p$. In particular, under certain technical conditions applicable to any root datum we construct…

We show that if 2^{aleph_0} Cohen reals are added to the universe, then for every reduced non-free torsion-free abelian group A of cardinality less than the continuum, there is a prime p so that Ext_p(A, Z) not= 0. In particular if it is…

We extend \cite[Theorem 4.5]{DGNO} and \cite[Theorem 4.22]{LKW} to positive characteristic (i.e., to the finite, not necessarily fusion, case). Namely, we prove that if $\D$ is a finite non-degenerate braided tensor category over an…

Let $\Cr_\Q(2)$ be the Cremona group of rank $2$ over rational numbers. we give a classification of large finite subgroups $G$ of $\Cr_\Q(2)$ and give a new sharp bound smaller (but not multiplicative) than $M(\Q)=120960 =…

Let $p$ be a prime, $D$ a finite dimensional noncommutative division $\mathbb{Q}_p$-algebra, and $SL_1(D)$ the group of elements of $D$ of reduced norm $1$. When the center of $D$ is $\mathbb{Q}_p$, we prove that no open subgroup of…

Let BG be a classifying variety for an exceptional simple simply connected algebraic group G. We compute the degree 3 unramified Galois cohomology of BG with values in Q/Z(2) over an arbitrary field F. Combined with a paper by Merkurjev,…

Let C be the complex field and K=C((x,y)) or K=C((x))(y). Let G be a connected linear algebraic group over K. Under the assumption that the K-variety G is K-rational, i.e. that the function field is purely transcendant, it was proved that a…

We study irreducible subvarieties of the universal hypersurface $\mathcal{X}/B$ of degree $d$ and dimension $n$. We prove that when $d$ is sufficiently large, a degree $kd$ subvariety $Z$ which dominates $B$ comes from intersection with a…

A (left) Engel sink of an element g of a group G is a subset containing all sufficiently long commutators [...[[x,g],g],...,g], where x ranges over G. We prove that if p is a prime and G a finite group in which, for some positive integer m,…

Given an infinite topological group G and a cardinal k>0, we say that G is almost k-free if the set of k-tuples in G^k which freely generate free subgroups of G is dense in G^k. In this note we examine groups having this property and…

The Steinitz class of a number field extension K/k is an ideal class in the ring of integers O_k of k, which, together with the degree [K:k] of the extension determines the O_k-module structure of O_K. We call R_t(k,G) the classes which are…

Let $H(2,1;\underline{t})$ be Hamiltonian superalgebras over $\mathbb{F}$, an algebraically closed field of prime characteristic $p>3$, which are non-restricted simple Lie superalgebras, generally. In this paper, we study generalized…

We present basic properties of Gr\"obner bases of submodules of a free module of finite rank over a polynomial ring $R$ with coefficients in a graded truncated discrete valuations ring $A$. As an application, we give a criterion for a…

Let $p$ be an odd prime and $L/K$ a $p$-adic Lie extension whose Galois group is of the form $\mathbb{Z}_p^{d-1}\rtimes \mathbb{Z}_p$. Under certain assumptions on the ramification of $p$ and the structure of an Iwasawa module associated to…

For $p$ a prime and $a\in\mathbb{Q}$, where $a$ is not a $p^n$-th power of any rational number, the extension $\mathbb{Q}(w_n)/\mathbb{Q}$ where $w_n=\root p^n \of a$ is separable but non-normal. The Hopf-Galois theory for separable…

In this paper we show how to construct, for most p >= 5, two types of surjective representations \rho:G_Q=Gal(\bar{Q}/Q) -> GL_2(Z_p) that are ramified at an infinite number of primes. The image of inertia at almost all of these primes will…

Suppose $K$ is a finite field extension of $\mathbb{Q} _p$ containing a primitive $p$-th root of unity. Let $\Gamma _{<p}$ be the Galois group of a maximal $p$-extension of $K$ with the Galois group of period $p$ and nilpotent class $<p$.…

Let $G$ be an algebraic group of classical type of rank $l$ over an algebraically closed field $K$ of characteristic $p$. We list and determine the dimensions of all irreducible $KG$-modules $L$ with $\dim L < \binom{l+1}{4}$ if $G$ is of…