arXiv subjects

Stella Anevski

Publications and source records attributed to Stella Anevski.

4 recordsLinked to original sources

arXiv2012

On the algebraic K-theory of Spec Z^N

In his thesis, N. Durov develops a theory of algebraic geometry in which schemes are locally determined by commutative algebraic monads. In this setting, one is able to construct the Arakelov geometric compactification of the spectrum of the ring of integers in a purely algebraic fashion. This object arises as the limit of a certain projective system of generalized schemes. We study the constituents of this projective system, and compute their algebraic K-theory.

math.AG↗

arXiv2011

Reconstruction of quasi-compact quasi-separated schemes from categories of perfect complexes

We show how to recover the underlying topological space of a quasi-compact quasi-separated scheme from the tensor triangulated structure on its category of perfect complexes.

math.AG↗

arXiv2011

Reconstructing the spectrum of F_1 from the stable homotopy category

The finite stable homotopy category S_0 has been suggested as a candidate for a category of perfect complexes over the monoid scheme Spec F_1. We apply a reconstruction theorem from algebraic geometry to S_0, and show that one recovers the one point topological space. We also classify filtering subsets of the set of principal thick subcategories of S_0, and of its p-local versions. This is motivated by a result saying that the analogous classification for the category of perfect complexes over an affine scheme provides topological information.

math.AG↗

arXiv2009

Riemann-Roch and Riemann-Hurwitz theorems for global fields

In this paper, we use counting theorems from the geometry of numbers to extend the Riemann-Roch theorem and the Riemann-Hurwitz formula to global fields of arbitrary characteristic.

math.NT↗