9 problems

Let $k$ be a $\sigma$-field and $R$ a finitely $\sigma$-generated $k$-$\sigma$-algebra. A $\sigma$-ideal is radical if it is radical as an ordinary ideal, and mixed if, whenever…

Let $k$ be an algebraically closed field, let $V$ be a variety over $k$, and let $(V,\phi)$ be a $\sigma$-variety over $k$, with $\phi$ the self-map defining its difference structu…

Pellarin's expansion conjecture. For all $n\in\mathbb{N}^*$ and $\Sigma\subset\mathbb{N}^*$ satisfying $|\Sigma|\equiv n\pmod{q-1}$, there is a unique expansion

Let $K$ be a difference field and let $R$ be a finitely difference generated difference algebra over $K$. A difference ideal in $R$ is radical well-mixed if it is both radical and…

Dichotomy conjecture. Either $f$ or $\exp_C(f)$ is regularly $\mu$-transcendental over $K_s$.

Regular-independence conjecture. Every finite subset of this set is regularly $\mu$-independent over $K_s$.

Operator-theoretic generalization of Denis–Schanuel's conjecture. The asserted regular $\mu$-independence holds.

Let $k$ be a $\sigma$-field and $R$ a finitely $\sigma$-generated $k$-$\sigma$-algebra. A prime … of $R$ is minimal if every prime … with $\subset$ satisfies $=$. Minimal-prime fin…

Let $(X,\sigma)$ be a finite-dimensional difference scheme of finite $\sigma$-type over a finite difference field $(k,\varphi_0)$, where $\varphi_0$ is the distinguished Frobenius…