arXiv subjects

Azur Đonlagić

Publications and source records attributed to Azur Đonlagić.

3 recordsLinked to original sources

arXiv2026

Numerical Calculation of Periods on Schoen's Class of Calabi-Yau Threefolds

Through classical modularity conjectures, the period integrals of a holomorphic $3$-form on a rigid Calabi-Yau threefold are interesting from the perspective of number theory. Although the (approximate) values of these integrals would be very useful for studying such relations, they are difficult to calculate and generally not known outside of the rare cases in which we can express them exactly. In this paper, we present an efficient numerical method to compute such periods on a wide class of Calabi-Yau threefolds constructed by small resolutions of fiber products of elliptic surfaces over $\mathbf{P}^1$, introduced by C. Schoen in his 1988 paper. Many example results are given, which can easily be calculated with arbitrary precision. We provide tables in which each result is written to a precision of 30 decimal places and then compared to integrals of the appropriate modular form, to confirm accuracy.

math.AG↗

arXiv2026

Separable Pseudo-reductive Bands with Applications to Rational Points

We extend the Galois-theoretic Borovoi-Springer interpretation of algebraic bands to a class of étale-locally represented bands on the fppf site of an arbitrary field $k$, which we call separable bands. Next, a band represented étale-locally over $k$ by a pseudo-reductive group is shown to be globally representable when $[k : k^p] = p$, with counterexamples in general. When $k$ is a global or local field, we deduce a generalization of Borovoi's abelianization theory to separable bands represented by smooth connected algebraic groups. As an application, we prove that the Brauer-Manin obstruction is the only obstruction to both the Hasse principle and weak approximation on a homogeneous space of a pseudo-reductive group (more generally, of a smooth connected affine algebraic group with split unipotent radical) having a smooth connected geometric stabilizer.

math.NT↗

arXiv2025

Brauer-Manin obstructions for homogeneous spaces of commutative affine algebraic groups over global fields

Questions related to Brauer-Manin obstructions to the Hasse principle and weak approximation for homogeneous spaces of tori over a number field are well-studied, generally using arithmetic duality theorems, starting with works of Sansuc and of Colliot-Thélène. In this article, we prove the analogous statements (and include obstructions to strong approximation over finite places) in the general case of a commutative affine group scheme $G$ of finite type over a global field in any characteristic. We also study finiteness of different variants of the second Tate-Shafarevich kernel (such as $S$-kernels and $ω$-kernels) of the Cartier dual of $G$. All this is made possible by some recent theoretical advancements in positive characteristic, namely the finiteness theorems of B. Conrad and the generalized Tate duality of Z. Rosengarten.

math.NT↗