Local Flat Duality of Abelian Varieties.
Local fundamental groups of surface singularities in characteristic p.
Local generalizations of Lefschetz-Zariski theorems.
Local geometry of smooth curves passing through rational double points.
Local geometry of zero sets of holomorphic functions near the torus.
Local heights on Abelian varieties and rigid analytic uniformization.
Local heights on Momford curves.
Local Holomorphic Factorization for Free Conformal Fields
Local homology and cohomology on schemes
Local Indecomposability of Hilbert Modular Galois Representations
We prove the indecomposability of the Galois representation restricted to the -decomposition group attached to a non CM nearly -ordinary weight two Hilbert modular form over a totally real field under the assumption that either the degree of over is odd or the automorphic representation attached to the Hilbert modular form is square integrable at some finite place of .
Local L-factors of motives and regularized determinants.
Local moduli for plane curve singularities, the dimension of the ...-constant stratum.
Local monodromy in non-archimedean analytic geometry
Local monomialization of transcendental extensions
Suppose that are regular local rings which are essentially of finite type over a field of characteristic zero. If is a valuation ring of the quotient field of which dominates , then we show that there are sequences of monoidal transforms (blow ups of regular primes) and along such that is a monomial mapping. It follows that a morphism of nonsingular varieties can be made to be a monomial mapping along a valuation, after blow ups of nonsingular subvarieties.
Local properties of licci ideals.
Local semianalytic geometry.
Local Structure of Brill-Noether Strata in the Moduli Space of Flat Stable Bundles
Local structure of the moduli space of vector bundles over curves.
Local symplectic algebra of quasi-homogeneous curves
We study the local symplectic algebra of parameterized curves introduced by V. I. Arnold. We use the method of algebraic restrictions to classify symplectic singularities of quasi-homogeneous curves. We prove that the space of algebraic restrictions of closed 2-forms to the germ of a 𝕂-analytic curve is a finite-dimensional vector space. We also show that the action of local diffeomorphisms preserving the quasi-homogeneous curve on this vector space is determined by the infinitesimal action of...
Local units, elliptic units, Heegner points and elliptic curves.