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Stepan Nesterov

Publications and source records attributed to Stepan Nesterov.

2 recordsLinked to original sources
arXiv2026

Mod p Monodromy of Cyclic Covers of the Projective Line

In this paper, we prove a big monodromy theorem for the monodromy of cyclic coverings of projective line for cohomology with Fp-coefficients. This is a direct generalization of the results of Achter and Pries, where such a theorem is proved for cyclic coverings of degree 2 and 3. Instead of generalizing their methods, we adapt the proof of the analogous theorem for integral cohomology. In our subsequent work, we will apply this theorem to construct in infinitely many cases Galois extensions of Q with Galois group PSL(n, q) and PSU(n, q), where q can be an arbitrarilty large prime power.

math.NT↗
arXiv2026

Simple Lie Groups of type An as Galois groups over Q

In this paper, we utilize our previous results on mod p monodromy of cyclic coverings of the projective line to realize a large series of groups of the form PSL(n, q) and PSU(n, q) as Galois groups over Q. We achieve for the first time a fully explicit infinite series of such groups where simultaneously the field can have arbitrarily large degree over the prime field and the group does not coincide with PGL(n, q) or PGU(n, q), respectively.

math.NT↗