— In his previous papers [19, 21, 23, 25] the author proved that in characteristic different of 2 the jacobian J(C) of a hyperelliptic curve C with equation y2 = f(x) has only trivial endomorphisms over an algebraic closure of the ground field K if the Galois group Gal(f) of the irreducible polynomial f with coefficients in K is either the full symmetric group or the alternating group on n elem...

Let F be a local non-archimedean field and let G be the group of F valued points of a connected reductive algebraic group over F. In this paper we compute the Ext-groups of generalized Steinberg representations in the category of smooth G-representations with coefficients in a certain self-injective ring. AMS 2000 Mathematics subject classification: Primary 22E50. Secondary 11F70.

On promoting the type IIA side of the N = 1 Heterotic/type IIA dual pairs of [1] to M-theory on a 'barely G 2 Manifold' of [2], by spectrum-matching we show a possible triality between Heterotic on a self-mirror Calabi-Yau, M-theory on the above 'barely G 2-Manifold' constructed from the Calabi-Yau on the type IIA side and F-theory on an elliptically fibered Calabi-Yau 4-fold fibered over a tri...

We determine which simple algebraic groups of type D4 over arbitrary fields of characteristic different from 2 admit outer automorphisms of order 3, and classify these automorphisms up to conjugation. The criterion is formulated in terms of a representation of the group by automorphisms of a trialitarian algebra: outer automorphisms of order 3 exist if and only if the algebra is the endomorphis...