131 citations · 953 across the 64 of their papers we have counts for
9 papers · 1 filter
Noncommutative Kummer theory
Leonid Positselski
We discuss lifting properties of continuous homomorphisms from absolute Galois groups into (pro)finite groups. An analogy with the Langlands program is pointed out in the beginning…
Koszulity of cohomology = -ness + quasi-formality
Leonid Positselski
This paper is a greatly expanded version of Section 9.11 in arXiv:1006.4343. A series of definitions and results illustrating the thesis in the title (where quasi-formality means v…
Koszul property and Bogomolov's conjecture
Leonid Positselski
This is an enhanced version of the author's 1998 Harvard Ph.D. thesis, as published by IMRN in 2005. We propose an extension of Bogomolov's conjecture about commutator subgroups of…
Categorical Bockstein sequences
Leonid Positselski
We construct the reduction of an exact category with a twist functor with respect to an element of its graded center in presence of an exact-conservative forgetful functor annihila…
Artin-Tate motivic sheaves with finite coefficients over an algebraic variety
Leonid Positselski
We propose a construction of a tensor exact category F_X^m of Artin-Tate motivic sheaves with finite coefficients Z/m over an algebraic variety X (over a field K of characteristic…
Galois cohomology of a number field is Koszul
Leonid Positselski
We prove that the Milnor ring of any (one-dimensional) local or global field K modulo a prime number l is a Koszul algebra over Z/l. Under mild assumptions that are only needed in…
The algebra of closed forms in a disk is Koszul
Leonid Positselski
We prove that the algebra of closed differential forms in an (algebraic, formal, or analytic) disk with logarithmic singularities along several coordinate hyperplanes is (both nont…
Mixed Artin-Tate motives with finite coefficients
Leonid Positselski
The goal of this paper is to give an explicit description of the triangulated categories of Tate and Artin-Tate motives with finite coefficients Z/m over a field K containing a pri…
Galois cohomology of certain field extensions and the divisible case of Milnor-Kato conjecture
Leonid Positselski
We prove the "divisible case" of the Milnor-Bloch-Kato conjecture (which is the first step of Voevodsky's proof of this conjecture for arbitrary prime l) in a rather clear and elem…