16 citations · 46 across the 13 of their papers we have counts for
13 papers
Algebraic dependence and Milnor K-theory
Adam Topaz
This paper shows that algebraic (in)dependence is encoded in Milnor K-theory of fields. As an application, we show that the isomorphism type of a field is determined by its Milnor…
Line and Hyperplane GT-variants
Florian Pop, Adam Topaz
In this work, we introduce a variant of the Grothendieck-Teichm{ü}ller group, defined in terms of complements of hyperplane arrangements and pro- two-step nilpotent fundament…
Recovering function fields from their integral -adic cohomology with the Galois action
Adam Topaz
In this note, we consider function fields of higher-dimensional algebraic varieties defined over non-local fields, and show how the Galois action on the cohomology such function fi…
Invariant hypersurfaces
Jason Bell, Rahim Moosa, Adam Topaz
The following theorem, which includes as very special cases results of Jouanolou and Hrushovski on algebraic -varieties on the one hand, and of Cantat on rational dynamics on th…
A Torelli Theorem for Higher-Dimensional Function Fields
Adam Topaz
We prove a Torelli-like theorem for higher-dimensional function fields, from the point of view of "almost-abelian" anabelian geometry.
Four-fold Massey products in Galois cohomology
Pierre Guillot, Jan Minac, Adam Topaz +1
In this paper, we develop a new necessary and sufficient condition for the vanishing of 4-Massey products of elements in the mod-2 Galois cohomology of a field. This new descriptio…
The Galois action on geometric lattices and the mod- I/OM
Adam Topaz
This paper studies the Galois action on a special lattice of geometric origin, which is related to mod- abelian-by-central quotients of geometric fundamental groups of variet…
Abelian-by-Central Galois Groups of Fields II: Definability of Inertia/Decomposition Groups
Adam Topaz
This paper explores some first-order properties of commuting-liftable pairs in pro- abelian-by-central Galois groups of fields. The main focus of the paper is to prove that m…
Reconstructing function fields from rational quotients of mod- Galois groups
Adam Topaz
In this paper, we develop the main step in the global theory for the mod- analogue of Bogomolov's program in birational anabelian geometry for higher-dimensional function fie…
Abelian-by-Central Galois groups of fields I: a formal description
Adam Topaz
Let be a field whose characteristic is prime to a fixed integer with , and choose a primitive th root of unity. Denote the absolute Galois grou…
Commuting-Liftable Subgroups of Galois Groups II
Adam Topaz
Let denote either a positive integer or , let be a fixed prime and let be a field of characteristic different from . In the presence of sufficiently ma…
Galois Module Structure of \Z/\ell^n-th Classes of Fields
Jan Minac, John Swallow, Adam Topaz
In this paper we use the Merkurjev-Suslin theorem to explore the structure of arithmetically significant Galois modules that arise from Kummer theory. Let K be a field of character…
Almost-Commuting-Liftable Subgroups of Galois Groups
Adam Topaz
Let K be a field and \ell be a prime such that char K \neq \ell. In the presence of sufficiently many roots of unity in K, we show how to recover some of the inertia/decomposition…