Galois subspaces for smooth projective curves

Right-projective Hulls and Galois Galois Theory

Let N be a bijective measure space. D. Sasaki’s classification of positive definite, globally universal domains was a milestone in homological Galois theory. We show that |O| ≤ K. The groundbreaking work of H. Thomas on contra-arithmetic planes was a major advance. Recent developments in analytic group theory [36, 36] have raised the question of whether Fréchet’s conjecture is false in the cont...

Totally Reflexive Modules Constructed from Smooth Projective Curves of Genus

In this paper, from an arbitrary smooth projective curve of genus at least two, we construct a non-Gorenstein Cohen-Macaulay normal domain and a nonfree totally reflexive module over it.

Galois Theory and Projective Geometry

We explore connections between birational anabelian geometry and abstract projective geometry. One of the applications is a proof of a version of the birational section conjecture. Invited paper for the special volume of Communications on Pure and Applied Mathematics for 75th Anniversary of the Courant Institute

On smooth fuzzy subspaces

A Note on Galois Modules and the Algebraic Fundamental Group of Projective Curves

Let X be a smooth projective connected curve of genus g ≥ 2 defined over an algebraically closed field k of characteristic p > 0. Let G be a finite group, P a Sylow p-subgroup of G and NG(P ) its normalizer in G. We show that if there exists an étale Galois cover Y → X with group NG(P ), then G is the Galois group wan étale Galois cover Y → X , where the genus of X depends on the order of G, th...