Spherical spaces for which the Hasse principle and weak approximation fail.
We construct spherical homogeneous spaces X of semisimple simply connected groups with connected stabilizers such that the Hasse principle or weak approximation fail for X.
Erratum : On the Hasse principle for homogeneous spaces with finite stabilizers
On the Hasse principle for homogeneous spaces with finite stabilizers
Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.
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