T. Kowalczyk

activity

20182023

most citedSums of even powers of k-regulous functions

3 citations · 7 across the 3 of their papers we have counts for

collaborators

4 papers

math.AG2023★ 2 cited

Sums of squares on hypersurfaces

Kacper Błachut, Tomasz Kowalczyk

We show that the Pythagoras number of rings of type $R [x, y, f (x, y)]$ is infinite, provided that the polynomial $f (x, y)$ satisfies some mild conditions.

math.AC2022★ 2 cited

On Waring numbers of henselian rings

Tomasz Kowalczyk, Piotr Miska

Let $n > 1$ be a positive integer. Let $R$ be a henselian local ring with residue field $k$ of $n$ th level $s_{n} (k)$ . We give some upper and lower bounds for the $n$ th Waring number $…

math.AG2020★ 3 cited

Sums of even powers of k-regulous functions

Juliusz Banecki, Tomasz Kowalczyk

We provide an example of a nonnegative $k$ -regulous function on $R^{n}$ for $k \geq 1$ and $n \geq 2$ which cannot be written as a sum of squares of $k$ -regulous functions. W…

math.AG2018

Blown-up Čech cohomology and Cartan's Theorem B on real algebraic varieties

Tomasz Kowalczyk

We introduce a concept of blown-up Čech cohomology for coherent sheaves of homological dimension $\leq 1$ and some quasi-coherent sheaves on a non-singular real affine variety. Its…