81 research outputs found
Factorization theorems for the representations of the fundamental groups of quasiprojective varieties and some applications
In this paper, using Gromov-Jost-Korevaar-Schoen technique of harmonic maps
to nonpositively curved targets, we study the representations of the
fundamental groups of quasiprojective varieties. As an application of the above
considerations we give a proof of a weak version of the Shafarevich Conjecture.Comment: 50 pages, LaTe
Orlov spectra as a filtered cohomology theory
This paper presents a new approach to the dimension theory and Orlov spectra
of triangulated categories by considering natural filtrations that arise in the
pretriangulated setting.Comment: 27 pages, 2 figure
Complex projective surfaces and infinite groups
The paper contains a general construction which produces new examples of non
simply-connected smooth projective surfaces. We analyze the resulting surfaces
and their fundamental groups. Many of these fundamental groups are expected to
be non-residually finite. Using the construction we also suggest a series of
potential counterexamples to the Shafarevich conjecture which claims that the
universal covering of smooth projective variety is holomorphically convex. The
examples are only potential since they depend on group theoretic questions,
which we formulate, but we do not know how to answer. At the end we formulate
an arithmetic version of the Shafarevich conjecture.Comment: 29 pages, some comments and examples added LaTeX 2.0
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