3 citations · 8 across the 13 of their papers we have counts for
6 papers · 1 filter
Elliptic groups and rings
Ilia Pirashvili
As it is well known, one can define an abelian group on the points of an elliptic curve, using the so called chord-tangent law \cite{dale}, and a chosen point. However, that very c…
The fundamental group of binoid varieties
Holger Brenner, Ilia Pirashvili
Binoid schemes generalise monoid schemes, which in turn enable us to generalise toric varieties. Let be a binoid scheme. The aim of this paper is to calculate the topological f…
On the group of separable quadratic algebras and stacks
Ilia Pirashvili
The aim of this paper is to study the group of isomorphism classes of torsors of finite flat group schemes of rank 2 over a commutative ring . This, in particular, generalises t…
The Étale Fundamental Groupoid as a Terminal Costack
Ilia Pirashvili
Let be a noetherian scheme. We denote by the fundamental groupoid. In this paper we prove that the assignments is the 2-terminal costack over the site…
On Cohomology and vector bundles over monoid schmes
Ilia Pirashvili
The aim of this paper is to study the cohomology theory of monoid schemes in general and apply it to vector and line bundles. We will prove that over separated monoid schemes, any…
On the spectrum of monoids and semilattices
Ilia Pirashvili
Our main observation is that the contravariant functor Spec on the category of commutative monoids is representable. We discuss a few consequences of this fact. In particular, we g…