An exotic smooth structure on .
An explicit algebraic family of genus-one curves violating the Hasse principle
We prove that for any , the curvein is a genus curve violating the Hasse principle. An explicit Weierstrass model for its jacobian is given. The Shafarevich-Tate group of each contains a subgroup isomorphic to .
An explicit factorisation of the zeta functions of Dwork hypersurfaces
An explicit formula for period determinant
We consider a generic complex polynomial in two variables and a basis in the first homology group of a nonsingular level curve. We take an arbitrary tuple of homogeneous polynomial 1-forms of appropriate degrees so that their integrals over the basic cycles form a square matrix (of multivalued analytic functions of the level value). We give an explicit formula for the determinant of this matrix.
An explicit formula for the Hilbert symbol of a formal group
A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ()-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ()-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas for the...
An explicit version of Birch's Theorem
An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma
An expression for the superposition of general algebraic functions in terms of hypergeometric series.
An extension of Aritn-Verdier duality to non-torsion sheaves.
An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras
We prove an extension of Rais' theorem on the coadjoint representation of certain graded Lie algebras. As an application, we prove that, for the coadjoint representation of any seaweed subalgebra in a general linear or symplectic Lie algebra, there is a generic stabiliser and the field of invariants is rational. It is also shown that if the highest root of a simple Lie algerba is not fundamental, then there is a parabolic subalgebra whose coadjoint representation do not...
An extension of the Apéry number supercongruence
An extension to fields of positive characteristic of Mather's construction of the Thom-Boardman sequence
An extremal property of Rokhlin' s inequality for real algebraic curves.
An idempotent algorithm for a class of network-disruption games
A game is considered where the communication network of the first player is explicitly modelled. The second player may induce delays in this network, while the first player may counteract such actions. Costs are modelled through expectations over idempotent probability measures. The idempotent probabilities are conditioned by observational data, the arrival of which may have been delayed along the communication network. This induces a game where the state space consists of the network delays. Even...
An improved bound for the degree of smooth surfaces in not of general type
An improved Briancon-Skoda theorem with applications to the Cohen-Macaulayness of Rees algebras.
An improved tableau criterion for Bruhat order.
An Inequality of Chern Numbers for Open Algebraic Varieties.
An infinite dimensional Hodge-Tate theory
An infinite family of elliptic curves over Q with large rank via Néron's method.