The étale symmetric Künneth theorem

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

Notes on Étale Cohomology

à 4.0 Short Comment on Sheaves, Bundles, and Representable Functors. The notion of a sheaf over a topological space X generalize that of a bundle over X . We're more-or-less aware of this. I want to spend some time looking the specifics of this generalization. I'll focus on schemes. Fix a ring A and let 1 :=A 1 be the affine line. The first thing I want to point out is that the global section...

Symmetric Versions of Laman's Theorem

Recent work has shown that if an isostatic bar and joint framework possesses non-trivial symmetries, then it must satisfy some very simply stated restrictions on the number of joints and bars that are ‘fixed’ by various symmetry operations of the framework. For the group C3 which describes 3-fold rotational symmetry in the plane, we verify the conjecture proposed in [4] that these restrictions ...

Étale Lattices over Quadratic Integers

We construct lattices with quadratic structure over the integers in quadratic number fields having the property that the rank of the quadratic structure is constant and equal to the rank of the lattice in all reductions modulo maximal ideals. We characterize the case in which such lattices are free. The construction gives a representative of the genus of such lattices as an orthogonal sum of “s...

Beurling’s Theorem for Riemannian Symmetric Spaces Ii

We prove two versions of Beurling’s theorem for Riemannian symmetric spaces of arbitrary rank. One of them uses the group Fourier transform and the other uses the Helgason Fourier transform. This is the master theorem in the quantitative uncertainty principle.