arXiv subjects

Nikita Geldhauser

Publications and source records attributed to Nikita Geldhauser.

6 recordsLinked to original sources

arXiv2026

Motives, cohomological invariants and the Freudenthal magic square

We investigate cohomological invariants and motivic invariants of semisimple algebraic groups arising in the Freudenthal magic square. Besides, we show that if the Rost invariant of a strongly inner group of type $E_7$ is a sum of at most two symbols modulo $2$, then it is isotropic over an odd degree field extension, and use this fact to give a different proof of a result of Petrov and Rigby. Moreover, we give a motivic interpretation of a result of Garibaldi and Petersson about a cohomological invariant of degree $5$ for certain groups of type $^2E_6$ which detects their isotropy.

math.AG↗

arXiv2025

$J$-invariant of linear algebraic groups of outer type

We extend the notion of the $J$-invariant to arbitrary semisimple linear algebraic groups and provide complete decompositions for the normed Chow motives of all generically quasi-split twisted flag varieties. Besides, we establish some combinatorial patterns for normed Chow groups and motives and provide some explicit formulae for values of the $J$-invariant.

math.AG↗

arXiv2024

Chow rings of quasi-split geometrically almost simple algebraic groups

We compute the Chow ring of a quasi-split geometrically almost simple algebraic group assuming the coefficients to be a field. This extends the classical computation for split groups done by Kac to the non-split quasi-split case. For the proof we introduce and study equivariant conormed Chow rings, which are well adapted to the study of quasi-split groups and their homogeneous varieties.

math.AG↗

arXiv2024

Morava $J$-invariant

We compute the co-multiplication of the algebraic Morava K-theory for split orthogonal groups. This allows us to compute the decomposition of the Morava motives of generic maximal orthogonal Grassmannians and to compute a Morava K-theory analogue of the $J$-invariant in terms of the ordinary (Chow) $J$-invariant.

math.KT↗

arXiv2024

Tits construction and Rost invariant

We show a Springer type theorem for the variety of parabolic subgroups of type $1,2,6$ for all groups of type $E_6$. As far as we know this gives the first example for the validity of the Springer theorem for projective homogeneous varieties of type $^2E_6$ different from varieties of Borel subgroups. The proof combines several topics, notably the Rost invariant, a Tits construction, Cartan's symmetric spaces and indirectly the structure of the Chow motives of projective homogeneous varieties of exceptional type.

math.AG↗

arXiv2024

Morava K-theory of orthogonal groups and motives of projective quadrics

We compute the algebraic Morava K-theory ring of split special orthogonal and spin groups. In particular, we establish certain stabilization results for the Morava K-theory of special orthogonal and spin groups. Besides, we apply these results to study Morava motivic decompositions of orthogonal Grassmannians. For instance, we determine all indecomposable summands of the Morava motives of a generic quadric.

math.KT↗