Representability in supergeometry

Abstract

Abstract1 In this paper we use the notion of Grothendieck topology to present a unified way to approach representability in supergeometry, which applies to both the differential and algebraic settings.

Quotients of complex algebraic supergroups

“…Hence the etale topology is finer than the Zariski one. By the previous observation, we immediately have that a sheaf on the etale topology is a sheaf in the Zariski one, but not vice-versa (see [7] Sec. 2, Prop.…”

“…We now make some observations on Grothendieck topologies. For more details see [14] for the ordinary setting and [7] for the supergeometric one. Observation 3.4.…”

“…Similarly, we can define another Grothendieck topology by taking Zariski coverings, i.e. collections of open embeddings, and obtain the super Zariski site (see [7]). Notice that if U i −→ U is a Zariski covering of a superscheme, then it is also an etale covering.…”

“…The morphism a p induces a natural transformation G/H −→ Y , with G(Z)/H(Z) −→ Y (Z) injective for all Z. In general, it will not be surjective, however we have the following (see [14,7] for the notion of sheafification in this context).…”

The Chern–Simons current in time series of knots and links in proteins

“…Results are expressed in hyperbolic volume and hyperbola graph as relations between the parameters gene sequence evolution. With this model of Chern-Simons current in biology [20], we can give a new definition of Ramanujan-Jones-Laurent polynomials [21][22][23]. We use the homotopy class of hyperbolic knotted fundamental group [24,25] to define the obstruction curvature components of viral glycoprotein as transponson and retrotransposon [26][27][28][29].…”