Let L/Qp be a finite extension, and let G be a locally L-analytic group such as the L-points of an algebraic group over L. The categories of smooth and of finite-dimensional algebraic representations of G may be viewed as subcategories of the category of continuous representations of G in locally convex L-vector spaces. This larger category contains many interesting new objects, such as the act...

We discuss the Hilbert Irreducibility Theorem, presenting briefly a new approach which leads to novel conclusions, especially in the context of algebraic groups. After a short survey of the issues and of the known theory, we shall illustrate the main principles and mention some new results; in particular, we shall state a toric analogue of Bertini’s Theorem and a lifting theorem for rational po...

We extend non-emptyness and irreducibility of Hassett divisors to the moduli spaces M-polarizable cubic fourfolds for higher rank lattices M, which in turn provides a systematic approach describing irreducible components intersection divisors. show that Fermat fourfold is contained every divisor, yields new proof Hassett’s existence theorem special fourfolds. obtain an algorithm determine any t...

This means that for all n ≥ 2, there exists no first-order sentence Fn in the language Ln = (+,−,×,=, 0, 1, In) satisfying the following property: for any real algebraic variety V of R, if we interpret the n-ary predicate In by membership to V then R |= Fn if and only if V is irreducible. Our proof will imply that irreducibility remains undefinable even if we add the exponential function to Ln....

In this paper we introduce the notion of interval-valued (i.v.) fuzzy prime and semiprime ideals of a hypersemiring and study different properties of these two ideals. Finally, we examine the strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a hypersemiring and characterize the equivalence of primeness, strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a fu...

In this paper, based on algebraic arguments, a new proof of the spectral characterization of those real matrices that leave a proper polyhedral cone invariant [Trans. Amer. Math. Soc., 343 (1994), pp. 479–524] is given. The proof is a constructive one, as it allows us to explicitly obtain for every matrix A, which satisfies the aforementioned spectral requirements, an A-invariant proper polyhed...

The program of Langlands is studied here on the basis of: • new concepts of global class field theory related to the explicit construction of global class fields and of reciprocity laws; • the representations of the reductive algebraic groups GL(n) constituting the n-dimensional representations of the associated global Weil-Deligne groups; • a toroidal compactification of the conjugacy classes ...