Specific mechanical energy

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In algebraic geometry, given a smooth projective curve over a finite field Fq and a smooth affine group scheme G over it, the moduli stack of principal bundles over X, denoted by BunG, is an algebraic stack over the category of G-bundles on X that is given by:[1] for any Fq-algebra R,

R the category of (principal) G-bundles over the relative curve X×FqSpecR.

In particular, the category of Fq-points of BunG, that is, BunG(Fq), is the category of G-bundles over X. Similarly, the moduli stack of bundles is defined when the curve X is over the field of complex numbers.

It is known that BunG is a smooth stack.

Behrend's formula

This is a version of Lefschetz trace formula when X is over a finite field.

Notes

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References

Besides the obvious, there are

Further reading