Arithmetic geometry and p-adic differential equations form a dynamic nexus where number theory, algebraic geometry and p-adic analysis converge. This interdisciplinary field investigates the solutions ...

In this paper, we prove the decidability of the theory of ℚp in the language (+, −, ·, 0, 1, Pn(n ∈ ℕ)) expanded by a predicate for the multiplicative subgroup nℤ (where n is a fixed integer). There ...

Our research group is concerned with two lines of investigation: the construction and study of (new) cohomology theories for algebraic varieties and the study of various aspects of the Langlands ...

The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.

If we complete the rational numbers $\mathbb{Q}$ with respect to the standard absolute value, we obtain the reals $\mathbb{R}$, wich is a connected topological space ...