Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Pirashvili, Ilia"'
Autor:
Pirashvili, Ilia
The aim of this paper is to interpret the Grothendieck construction in the monoidal world. That is to say, we restrict the equivalence between fibred categories and pseudo functors to the case of categories having only a single object. On other way o
Externí odkaz:
http://arxiv.org/abs/2402.11644
Autor:
Pirashvili, Ilia
It is a well-known fact that the category $\mathsf{Cat}(\mathbf{C})$ of internal categories in a category $\mathbf{C}$ has a description in terms of crossed modules, when $\mathbf{C}=\mathbf{Gr}$ is the category of groups. The proof of this result he
Externí odkaz:
http://arxiv.org/abs/2401.01863
Autor:
Pirashvili, Ilia
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 chord-tangent law allows us to define a rather more obscure algebraic s
Externí odkaz:
http://arxiv.org/abs/2201.05553
Autor:
Pirashvili, Ilia
The aim of this paper is to study the points and localising subcategories of the topos of $M$-sets, for a finite monoid $M$. We show that the points of this topos can be fully classified using the idempotents of $M$. We introduce a topology on the is
Externí odkaz:
http://arxiv.org/abs/2011.11747
Autor:
Pirashvili, Ilia
We aim to reconstruct a monoid scheme $X$ from the category of quasi-coherent sheaves over it. This is much in the vein of Gabriel's original reconstruction theorem. Under some finiteness condition on a monoid schemes $X$, we show that the localising
Externí odkaz:
http://arxiv.org/abs/2002.04336
Autor:
Brenner, Holger, Pirashvili, Ilia
Binoid schemes generalise monoid schemes, which in turn enable us to generalise toric varieties. Let $X$ be a binoid scheme. The aim of this paper is to calculate the topological fundamental group of $KX$, where $K=\mathbb{C}$ or $\mathbb{R}$. For th
Externí odkaz:
http://arxiv.org/abs/1908.05538
Autor:
Pirashvili, Ilia
We compare the colimit and 2-colimit of strict 2-functors in the 2-category of groupoids, over a certain type of posets. These posets are of special importance, as they correspond to coverings of a topological space. The main result of this paper giv
Externí odkaz:
http://arxiv.org/abs/1905.11288
Autor:
Pirashvili, Ilia
This thesis is divided in two equal parts. We start the first part by studying the Kato-spectrum of a commutative monoid M, denoted by KSpec(M). We show that the functor M → KSpec(M) is representable and discuss a few consequences of this fact. In
Externí odkaz:
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.689373
Autor:
Pirashvili, Ilia
Publikováno v:
Math. Proc. Camb. Phil. Soc. 169 (2020) 31-74
Let $X$ be a monoid scheme. We will show that the stalk at any point of $X$ defines a point of the topos $\Qc(X)$ of quasi-coherent sheaves over $X$. As it turns out, every topos point of $\Qc(X)$ is of this form if $X$ satisfies some finiteness cond
Externí odkaz:
http://arxiv.org/abs/1611.02211