Algebraic geometry and local differential geometry
Algebraic Geometry - Selected Topics
Algebraic groups associated with abelian varieties.
Algebraic groups with a distinguished conjugacy class.
Algebraic homotopy classes of rational functions
Let be a field. We compute the set ofnaivehomotopy classes of pointed -scheme endomorphisms of the projective line . Our result compares well with Morel’s computation in [11] of thegroup of -homotopy classes of pointed endomorphisms of : the set admits an a priori monoid structure such that the canonical map is a group completion.
Algebraic -theory and crystalline cohomology
Algebraic -theory and etale cohomology
Algebraic K-Theory and Quadratic Forms.
Algebraic K-Theory Eventually Surjects onto Topological K-Theory.
Algebraic leaves of algebraic foliations over number fields
We prove an algebraicity criterion for leaves of algebraic foliations defined over number fields. Namely, consider a number field embedded in , a smooth algebraic variety over , equipped with a rational point , and an algebraic subbundle of the its tangent bundle , defined over . Assume moreover that the vector bundle is involutive, i.e., closed under Lie bracket. Then it defines an holomorphic foliation of the analytic manifold , and one may consider its leaf through . We prove...
Algebraic Legendrian varieties [Book]
Algebraic loop groups and moduli spaces of bundles
We study algebraic loop groups and affine Grassmannians in positive characteristic. The main results are normality of Schubert-varieties, the construction of line-bundles on the affine Grassmannian, and the proof that they induce line-bundles on the moduli-stack of torsors.
Algebraic methods in the theory of theta functions
Algebraic models of smooth manifolds.
Algebraic non-integrability of the Cohen map.
Algebraic number fields with the principal ideal condition
Algebraic points of abelian functions in two variables
Algebraic points of low degree on the Fermat quintic
Algebraic points on cubic hypersurfaces
Algebraic, Rational, and homological equivalence of real cycles.