In this paper, we prove effective estimates for the number of exceptional values and the totally ramified value number for the Gauss map of pseudo-algebraic minimal surfaces in Euclidean four-space and give a kind of unicity theorem.

We give an axiomatization of the first-order theory of the field of Witt vectors over the algebraic closure of a finite field, with the lifting of the Frobenius map.  2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS

The semi-topological K-theory of real varieties, KR(−), is an oriented multiplicative (generalized) cohomology theory which extends the authors’ earlier theory, K(−), for complex algebraic varieties. Motivation comes from consideration of algebraic equivalence of vector bundles (sharpened to real semi-topological equivalence), consideration of Z/2-equivariant mapping spaces of morphisms of alge...

We introduce equivariant Burnside groups, new invariants in birational geometry, generalizing symbols groups for actions of finite abelian due to Kontsevich, Pestun, and the second author, study their properties. establish a specialization map type smooth algebraic variety with an action group.

We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a “cohomology theory” for complex algebraic varieties. The theory is bigraded, functorial, and admits Gysin maps. It carries a natural cup product and a pairing to L-homology. Chern classes of algebraic bundles are defined in the theory. There is a na...

We organize colored aromatic trees into a pre-Lie–Rinehart algebra (i.e., flat torsion-free Lie–Rinehart algebra) endowed with natural trace map, and show the freeness of this object among algebras trace. This yields algebraic foundations B-series.

In the paper 10] (see also 2]), the authors construct a holomorphic map from the modular curve X(k) = H 2 =?(k), where ?(k) is the congruence subgroup of ? = PSL(2; Z), into the projective space C P (k?3 2) , via theta functions. This holomorphic map is equivariant with respect to the action of PSL(2; Z=k) on both factors, and extends to the conformal compactiication X(k). Thus, X(k) can be exh...

Explaining codon evolution in the standard genetic code is a remarkable subject in Molecular Biology. There are many works which try to develop a model to represent this evolution, sometimes using a certain amount of mathematical tools. The present work has as its main objective to explain one possible dynamical evolution model, which is based in the algebraic approach proposed in 1993 by Horno...

There are nontrivial dualities and parallels between polynomial algebras and the Grassmann algebras. This paper is an attempt to look at the Grassmann algebras at the angle of the Jacobian conjecture for polynomial algebras (which is the question/conjecture about the Jacobian set – the set of all algebra endomorphisms of a polynomial algebra with the Jacobian 1 – the Jacobian conjecture claims ...