My work deals with foundational aspects of motivic homotopy theory. Here are some details of the papers published or posted while being supported by the ERC project.

The paper [DFJK21] (with F. Déglise, J. Fasel, and A. Khan) establishes a number of properties of the motivic stable homotopy category with rational coefficients: absolute purity, constructibility, local duality and SL-orientability. The \(\mathbb{A}^1\)-bivariant groups are identified with the Borel-Moore type Chow-Witt groups rationally.

The two preprints [JX20] (with H. Xie) and [Jin20a] study questions related to real étale cohomology. In the work [JX20] we discuss the relation between coherent duality and real étale duality via a Gersten-type complex; this is relevant for many questions arising in the ERC project due to the connection of coherent duality with the pushforward maps in hermitian \(K\)-theory.

In the work [Jin20a], we compute the Grothendieck group of the rational motivic stable homotopy category for reasonable schemes.

In the work [Jin20b] we define trace maps and local terms in the stable motivic homotopy category over a general base scheme, and prove an analogue of a theorem of Varshavsky: for a contracting correspondence, the local term agrees with an invariant of simpler form called the naive local term; we also show that some invariants from \(\mathbb{A}^1\)-enumerative geometry, such as the \(\mathbb{A}^1\)-Brouwer local degree and the local Euler class, can be interpreted as local terms.


[DFJK21] F. Déglise, J. Fasel, F. Jin, A. Khan, On the rational motivic homotopy category, J. Ec. Polytech. Math. 8 (2021), 533-583.
Publically available at arXiv:2005.10147 math.AG doi 10.5802/jep.153


[JX20] F. Jin, H. Xie, A Gersten complex on real schemes, arXiv:2007.04625 math.AG

[Jin20a] F. Jin, On some finiteness results in real étale cohomology, arXiv:2009.00396 math.AG

[Jin20b] F. Jin, Local terms of the motivic Verdier pairing, arXiv:2010.09292 math.AG


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