An Algebraic Approach to the Residues in Algebraic Geometry.
An algebraic construction of the generic singularities of Boardman-Thom
An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity
Let be a germ of a complete intersection variety in , , having an isolated singularity at and be the germ of a holomorphic vector field having an isolated zero at and tangent to . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of is also isolated in the ambient space we give a formula for the homological index in terms of local linear algebra.
An algebraic method for calculating the topological degree
An algorithm for finding the Veech group of an origami.
An Algorithm for Lifting Points in a Tropical Variety
An algorithmic criterion for basicness in dimension 2.
An alternative description of the Drinfeld -adic half-plane
We show that the Deligne formal model of the Drinfeld -adic half-plane relative to a local field represents a moduli problem of polarized -modules with an action of the ring of integers in a quadratic extension of . The proof proceeds by establishing a comparison isomorphism with the Drinfeld moduli problem. This isomorphism reflects the accidental isomorphism of and for a two-dimensional split hermitian space for .
An alternative proof of Scheiderer's theorem on the Hasse principle for principal homogeneous spaces.
An alternative way to classify some Generalized Elliptic Curves and their isotopic loops
The Generalized Elliptic Curves are pairs , where is a family of triples of “points” from the set characterized by equalities of the form , where the law makes into a totally symmetric quasigroup. Isotopic loops arise by setting . When , identically is an entropic and is an abelian group. Similarly, a terentropic may be characterized by and is then a Commutative Moufang Loop . If in addition , we have Hall and is an exponent
An analog of the Fubini-Studi form for two-dimensional toric varieties.
An analogue of convexity for complements of amoebas of varieties of higher codimension, an answer to a question asked by B. Sturmfels.
An analogue of holonomic -modules on smooth varieties in positive characteristics.
An analogue of the Weierstrass ζ-function in characteristic p
An analytic construction of degenerating abelian varieties over complete rings
An analytic construction of degenerating curves over complete local rings
An analytic function and iterated integrals
An angle metric through the notion of Grassmann representative.
An annihilator for the -Selmer group by means of Heegner points
Let be a modular elliptic curve, and let be an imaginary quadratic field. We show that the -Selmer group of over certain finite anticyclotomic extensions of , modulo the universal norms, is annihilated by the «characteristic ideal» of the universal norms modulo the Heegner points. We also extend this result to the anticyclotomic -extension of . This refines in the current contest a result of [1].
An Application of a Theorem of Deuring and Safarevic.