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A variety $ X $ is $ F $-split if there exists an $ \mathcal{O}_{X} $-linear map $ \phi: F_{\ast}(\mathcal{O}_{X}) \to \mathcal{O}_{X} $ such that $ \phi \circ F^{\sharp} = \operatorname{id}_{\mathcal{O}_{X}} $. Such a map $ \phi $ is called a splitting. A closed sub-scheme $ Y $ of $ X $ is co...
In mathematics, a Frobenius splitting, introduced by Mehta and Ramanathan (1985), is a splitting of the injective morphism OX→F*OX from a structure sheaf OX of a characteristic p > 0 variety X to its image F*OX under the Frobenius endomorphism F*.
Brion & Kumar (2005) give a detailed discussion of Frobenius splittings.
A fundamental property of Frobenius-split projective schemes X is that the higher cohomology Hi(X,L) (i > 0) of ample line bundles L vanishes.
== References ==
Brion, Michel; Kumar, Shrawan (2005), Frobenius splitting methods in geometry and representation theory, Progres...
Two additional papers in combinatorics (That I managed to find on line) each having a beautiful and simple result.
On the Shannon Capacity of a Graph by Laszlo Lovasz
The Upper Bound Conjecture and Cohen Macaulay Rings by Richard Stanley
Convergence in the Fell topology is equivalent to convergence of matrix coefficients. In the finite-dimensional case, this is equivalent as $\rho_n(g) v \rightarrow \rho(g)v$.
Quote from Vogan (http://dedekind.mit.edu/~dav/iso3.pdf)
Suppose then that G is a real reductive Lie group. Write $\...
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Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm...
