Related papers: Triple Massey products vanish over all fields

We give a canonical procedure associating to an algebraic number a first a hyperelliptic curve C_a, and then a triangle curve (D_a, G_a) obtained through the normal closure of an associated Belyi function. In this way we show that the…

Let $K$ be a complete discretely valued field with mixed characteristic $(0, p)$ and imperfect residue field $k_K$. Let $\Delta$ be a finite set. We construct an equivalence of categories between finite dimensional…

We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…

We develop the foundations of effective ultraproducts of fields and their Galois groups using the methods of computability theory. These computability-theoretic analogs of ultraproducts are called cohesive products, since the role of an…

In this article, we investigate the shift of Abbes and Saito's ramification filtrations of the absolute Galois group of a complete discrete valuation field of positive characteristic under a purely inseparable extension. We also study a…

Let $f:S\to B$ be a fibration of curves and let $f_\ast\omega_{S/B}=\cU\oplus \cA$ be the second Fujita decomposition of $f.$ In this paper we study a kind of Massey products, which are defined as infinitesimal invariants by the cohomology…

Motivated by the study of trilinear forms for complex representations, we investigate the space of $G$-invariant linear forms on tensor products of irreducible admissible representations of $G = \mathrm{GL}_2(\mathbb{Q}_p)$ over…

We reprove and generalize the result that the intersection cohomology groups of a toric variety with coefficient in a nontrivial rank one local system vanish. We prove a similar vanishing result for a certain class of varieties on which a…

We examine which representations of the absolute Galois group of a field of finite characteristic with image over a finite field of the same characteristic may be constructed by the Galois group's action on the division points of an…

We continue the examination of the stable reduction and fields of moduli of G-Galois covers of the projective line over a complete discrete valuation field of mixed characteristic (0, p), where G has a cyclic p-Sylow subgroup P of order…

In this article, we study a certain Galois property of subextensions of $k(A_{\mathrm{tors}})$, the minimal field of definition of all torsion points of an abelian variety $A$ defined over a number field $k$. Concretely, we show that each…

We study the equivalence between infinitesimal Torelli theorem for smooth hypersurfaces in rational homogeneous varieties with Picard number one and the theory of generalized Massey products. This equivalence shows that the differential of…

Although the analogue of the theorem of Neukirch-Uchida for $p$-adic local fields fails to hold as it is, Mochizuki proved a certain analogue of this theorem for the absolute Galois groups with ramification filtrations of $p$-adic local…

Let $K/\mathbb{Q}$ be a finitely generated field of characteristic zero and $X/K$ a smooth projective variety. Fix $q\in\mathbb{N}$. For every prime number $\ell$ let $\rho_\ell$ be the representation of $\mathrm{Gal}(K)$ on the \'etale…

We prove that infinite Galois extensions of number fields with Galois group of finite exponent have the Northcott property. The main novelty of our approach lies in the application of a theorem of Segal on profinite groups.

In this paper, we investigate the maximal Cohen-Macaulay property of tensor products of modules, and then give criteria for projectivity of modules in terms of vanishing of Ext modules. One of the applications shows that the…

We provide a new condition for an absolutely almost simple algebraic group to have good reduction with respect to a discrete valuation of the base field which is formulated in terms of the existence of maximal tori with special properties.…

This is a revision of the paper that was previously entitled "Weighted Completion of Galois Groups and Some Conjectures of Deligne". Fix a prime number $\l$. We prove a conjecture stated by Ihara, which he attributes to Deligne, about the…

We classify all cubic function fields over any finite field, particularly developing a complete Galois theory which includes those cases when the constant field is missing certain roots of unity. In doing so, we find criteria which allow…

In various classes of infinite groups, we identify groups that are presentable by products, i.e. groups having finite index subgroups which are quotients of products of two commuting infinite subgroups. The classes we discuss here include…