9 papers
Deformation Theory of Monoid Schemes II: Precartesian Coextensions of Commutative Monoids
Ilia Pirashvili
This paper is a continuation of arXiv:2606.17088, where I studied precartesian coextensions of commutative monoids by systems of abelian groups. In this paper, we generalise it to…
Deformation Theory of Monoid Schemes I
Ilia Pirashvili
The aim of this paper is to develop a deformation theory of monoid schemes, generalising the approach developed by Grillet. The core idea of this approach is to introduce the notio…
n-ary elliptic groups, rings, and primes in arithmetic progressions
Ilia Pirashvili
I introduced the notion of an elliptic group in [Elliptic groups and rings. Beiträge zur Algebra und Geometrie 66(2), 497-529]. It is a quasi-group based on the tangent-chord law o…
Grothendieck's theory of fibred categories for monoids
Ilia Pirashvili
Grothendieck's theory of fibred categories establishes an equivalence between fibred categories and pseudo functors. It plays a major role in algebraic geometry and categorical log…
On internal categories and crossed objects in the category of monoids
Ilia Pirashvili
It is a well-known fact that the category of internal categories in a category has a description in terms of crossed modules, when $\mathbf{…
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…