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We establish p-adic versions of the Manin-Mumford conjecture, which states that an irreducible subvariety of an abelian variety with dense torsion has to be the translate of a subgroup by a torsion point. We do so in the context of certain rigid analytic s ...
We define and study in terms of integral IwahoriâHecke algebras a new class of geometric operators acting on the Bruhat-Tits building of connected reductive groups over p-adic fields. These operators, which we call U-operators, generalize the geometric n ...
We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...
We give a construction of an efficient one-out-of-many proof system, in which a prover shows that he knows the pre-image for one element in a set, based on the hardness of lattice problems. The construction employs the recent zero-knowledge framework of Ly ...
We define p-adic BPS or pBPS invariants for moduli spaces M-beta,M-chi of one-dimensional sheaves on del Pezzo and K3 surfaces by means of integration over a non-archimedean local field F. Our definition relies on a canonical measure mu can on the F-analyt ...
We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the solar system, ex ...
We construct "generalized Heegner cycles" on a variety fibered over a Shimura curve, defined over a number field. We show that their images under the p-adic Abel-Jacobi map coincide with the values (outside the range of interpolation) of a p-adic L-functio ...
The minimal faithful permutation degree (G) of a finite group G is the least nonnegative integer n such that G embeds in the symmetric group Sym(n). Clearly (G x H) (G) + (H) for all finite groups G and H. In 1975, Wright ([10]) proved that equality occurs ...
The special linear group G = SLn(Z[x(1), ... , x(k)]) (n at least 3 and k finite) is called the universal lattice. Let n be at least 4, and p be any real number in (1, infinity). The main result is the following: any finite index subgroup of G has the fixe ...