Utsav Choudhury

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math.AG2026

$A^{1}$ -fibration in algebraic geometry and $A^{1}$ -homotopy type

Utsav Choudhury, Aritra Mandal, Biman Roy

In this article we show that an $A^{1}$ bundle map or a vector bundle map $p : X \to Y$ induces trivial local fibration $S in g (X) \to S in g (Y)$ . Using t…

math.AG2024

A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks

Utsav Choudhury, Neeraj Deshmukh, Amit Hogadi

We develop a motivic cohomology theory, representable in the Voevodsky's triangulated category of motives, for smooth separated Deligne-Mumford stacks and show that the resulting h…

math.AG2024

$A^{1}$ -homotopy type of $A^{2} ∖ {(0, 0)}$

Utsav Choudhury, Biman Roy

In this article we prove that any $A^{1}$ -connected smooth $k$ -variety is $A^{1}$ -uniruled for any algebraically closed field $k$ . We establish that if a non empty op…

A1-fibration in algebraic geometry and A1-homotopy type

A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks

A1-homotopy type of A2∖{(0,0)}

$A^{1}$ -fibration in algebraic geometry and $A^{1}$ -homotopy type

$A^{1}$ -homotopy type of $A^{2} ∖ {(0, 0)}$