55 citations · 104 across the 16 of their papers we have counts for
16 papers · 1 filter
K_0-motives and the Chow weight-heart
Fangzhou Jin, Kunpeng Li
Bondarko and Luzgarev constructed the Chow weight structure on the homotopy category of -modules; we show that the heart of this weight structure is equivalent to the category…
Homological Milnor-Witt modules and Chow-Witt groups over general bases
Frédéric Déglise, Niels Feld, Fangzhou Jin
We introduce a general theory of homological Milnor-Witt cycle modules over an excellent base scheme equipped with a dimension function, extending both Rost's cycle modules and Fel…
Moving lemmas and the homotopy coniveau tower
Frédéric Déglise, Niels Feld, Fangzhou Jin
In this note we study the functoriality of the coniveau filtration in motivic homotopy theory via a moving lemma over a base scheme, extending previous works of Levine and Bachmann…
The quadratic Artin conductor of a motivic spectrum
Fangzhou Jin, Enlin Yang
Given a motivic spectrum over a smooth proper scheme which is dualizable over an open subscheme, we define its quadratic Artin conductor under some assumptions, and prove a for…
Perverse homotopy heart and MW-modules
Frédéric Déglise, Niels Feld, Fangzhou Jin
We compute the perverse delta-homotopy heart of the motivic stable homotopy category over a base scheme with a dimension function delta, rationally or after inverting the exponenti…
The limit and boundary characteristic classes in Borel-Moore motivic homology
Fangzhou Jin, Peng Sun, Enlin Yang
We show that the zero-dimensional part of the pro-Chern-Schwarz-MacPherson class defined by Aluffi can be lifted to the zeroth Suslin homology. The proof uses the pro-characteristi…
Some results on the motivic nearby cycle
Fangzhou Jin, Enlin Yang
We extend Ayoub's formalism of motivic nearby cycle functor to the -categorical level, and prove some desired cohomological properties by relating the motivic nearby cycle…
Trace maps in motivic homotopy and local terms
Fangzhou Jin
We define a trace map for every cohomological correspondence in the motivic stable homotopy category over a general base scheme, which takes values in the twisted bivariant groups.…
On some finiteness results in real étale cohomology
Fangzhou Jin
We show that for quasi-compact quasi-separated schemes of finite dimension, the constructibility condition in real étale cohomology agrees with a notion of constructibility arising…
A Gersten complex on real schemes
Fangzhou Jin, Heng Xie
We discuss a connection between coherent duality and Verdier duality via a Gersten-type complex of sheaves on real schemes, and show that this construction gives a dualizing object…
On the rational motivic homotopy category
Frédéric Déglise, Jean Fasel, Adeel A. Khan +1
We study the structure of the rational motivic stable homotopy category over general base schemes. Our first class of results concerns the six operations: we prove absolute purity,…
Borel isomorphism and absolute purity
Frédéric Déglise, Jean Fasel, Fangzhou Jin +1
We prove absolute purity for the rational motivic sphere spectrum. The main ingredient is the construction of an analogue of the Chern character, where algebraic K-theory is replac…
Künneth formulas for motives and additivity of traces
Fangzhou Jin, Enlin Yang
We prove several Künneth formulas in motivic homotopy categories and deduce a Verdier pairing in these categories following SGA5, which leads to the characteristic class of a const…
Algebraic G-theory in motivic homotopy categories
Fangzhou Jin
We prove that algebraic G-theory in is representable in unstable and stable motivic homotopy categories; in the stable category we identify it with the Borel-Moore theory associate…
Fundamental classes in motivic homotopy theory
Frédéric Déglise, Fangzhou Jin, Adeel A. Khan
We develop the theory of fundamental classes in the setting of motivic homotopy theory. Using this we construct, for any motivic spectrum, an associated bivariant theory in the sen…
Borel-Moore motivic homology and weight structure on mixed motives
Fangzhou Jin
By defining and studying functorial properties of the Borel-Moore motivic homology, we identify the heart of Bondarko-Hébert's weight structure on Beilinson motives with Corti-Hana…