@article{Karpenko_Merkurjev_2022, title={PoincarĂ© duality for tautological Chern subrings of orthogonal grassmannians}, volume={128}, url={https://www.mscand.dk/article/view/132376}, DOI={10.7146/math.scand.a-132376}, abstractNote={<p>Let $X$ be an orthogonal grassmannian of a nondegenerate quadratic form $q$ over a field. Let $C$ be the subring in the Chow ring $\text {CH}(X)$ generated by the Chern classes of the tautological vector bundle on $X$. We prove PoincarĂ© duality for $C$. For $q$ of odd dimension, the result was already known due to an identification between $C$ and the Chow ring of certain symplectic grassmannian. For $q$ of even dimension, such an identification is not available.</p>}, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Karpenko, Nikita A. and Merkurjev, Alexander S.}, year={2022}, month={Jun.} }