Dipankar Maity

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math.AG2026

On the internal homotopy theory of motivic categories

Dipankar Maity

We develop a general $\infty$ -categorical framework for internal Eilenberg-MacLane objects, internal homotopy groups, and an internal notion of covering spaces, and study their beh…

math.AG2026

Schematic Functorialities of Birational Motivic Homotopy Categories

Dipankar Maity

We promote the $n$ -birational motivic homotopy category assignment $S \mapsto H^{n} (S)$ to a $P r^{L}$ -valued presheaf on $C or r (Sch)_{ug l t, s m}$ . As a consequence, the…

math.AG2026

Birational Algebraic Topology

Dipankar Maity

Over a qcqs scheme $S$ , we analyze the birational localization $L_{bir} H^{A^{1}} (S)$ of the motivic $\infty$ -category $H^{A^{1}} (S)$ . We…