ion Techniques for Configuration Systems Rainer Weigel and Boi Faltings DRAFT Laboratoire d’Intelligence Artificielle Ecole Polytechnique F~d~rale de Lausanne (EPFL)

It is shown that in an infinite-dimensional dually separated second category topological vector space X there does not exist a probability measure μ for which the kernel coincides with X. Moreover, we show that in “good” cases the kernel has the full measure if and only if it is finitedimensional. Also, the problem posed by S. Chevet [5, p. 69] is solved by proving that the annihilator of the k...

In recent years the classification of elliptic curves over Q of various conductors has been attempted. Many results have shown that elliptic curves of a certain conductor do not exist. Later methods have concentrated on small conductors, striving to find them all and hence to verify the Shimura-Taniyama-Weil conjecture for those conductors. A typical case is the conductor 11. In [1], Agrawal, C...

In a series of papers, [25], [30], [28], [29], [31], [26], we showed that certain quantities from the arithmetic geometry of Shimura varieties associated to orthogonal groups occur in the Fourier coefficients of the derivative of suitable Siegel-Eisenstein series. It was essential in these examples that this derivative was the second term in the Laurent expansion of a Siegel-Eisenstein series a...

We prove that assuming the Colmez conjecture and “no Siegel zeros” conjecture, stable Faltings height of a CM abelian variety over number field is less than or equal to logarithm root discriminant definition times an effective constant depending only on dimension variety. In view fact for fields, averaged fields with no complex quadratic subfields are already proved, we unconditional analogues ...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...