The Symplectic Nature of the Space of Dormant Indigenous Bundles on Algebraic Curves

We study the symplectic nature of the moduli stack of dormant indigenous bundles on proper hyperbolic curves. Our aim of the present paper is to consider the positive characteristic analogue of work of S. Kawai (in the paper entitled “The symplectic nature of the space of projective connections on Riemann surfaces”), P. Arés-Gastesi, and I. Biswas. The main result asserts a certain compatibility of the symplectic structures between the moduli spaces involving dormant indigenous bundles. As an application of the result, we construct a Frobenius-constant quantization on the moduli stack of indigenous bundles over ordinary dormant curves. Facts, as Norwood Hanson says, are theory-laden; they are as theory-laden as we hope our theories are fact-laden. Or in other words, facts are small theories, and true theories are big facts. This does not mean, I must repeat, that right versions can be arrived at casually, or that worlds are built from scratch. We start, on any occasion, with some old version or world that we have on hand and that we are stuck with until we have the determination and skill to remake it into a new one. Some of the felt stubbornness of fact is the grip if habit: our firm foundation is indeed stolid. Worldmaking begins with one version and ends with another. Nelson Goodman, Ways of Worldmaking (1978)