Year: 2018
Type: preprint
Abstract: In this paper, we investigate the structure of the convergent quantization of the 1-shifted cotangent bundle $S$ of a smooth scheme $X$ over a perfect field of positive characteristic. The quantization is an $E_2$-algebra over the Frobenius twist $S'$ of the 1-shifted cotangent bundle which restricted to the zero section $X'\rightarrow S'$ is weakly $E_2$-Morita equivalent to the structure sheaf $\mathscr O_{X'}$ of the Frobenius twist $X'$ of $X$. Explicitly, we show that the $(\infty,2)$-category of coherent (left-)modules over $\mathscr O_{X'}$ is equivalent to the full subcategory of the $(\infty,2)$-category of coherent (left-)modules over the quantization restricted to the zero section generated by $\mathscr O_X$ are equivalent.
Source: arXiv (Cornell University)
Author: Hablicsek, Marton
Institution: Leiden University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2898474184