Moduli Spaces and Related Topics | Bridgeland Stability Conditions Applied to the Fargues–Fontaine Curve

Abstract：

The Fargues–Fontaine curve has become a fundamental geometric object in the study of p-adic Hodge theory. One of the key theories developed by Fargues and Fontaine concerns the stability condition for vector bundles on this curve. In this talk, we will apply Bridgeland stability conditions to the derived category of coherent sheaves on the Fargues–Fontaine curve. We will see that the Fargues–Fontaine curve presents a strong similarity to elliptic curves. Additionally, we will explore how the hearts defined by slicings of stability conditions generalize the notion of Banach–Colmez spaces. This talk is based on joint work with Qingyuan Jiang and Yucheng Liu.