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Article overview
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On the moduli stack of commutative, 1-parameter formal Lie group | Brian D. Smithling
; | Date: |
4 Sep 2007 | Abstract: | We attempt to develop a general algebro-geometric study of the moduli stack
of commutative, 1-parameter formal Lie groups, in full comportment with the
modern foundations of algebraic geometry. We emphasize the pro-algebraic
structure of this stack: it is the inverse limit, over varying n, of moduli
stacks of n-buds, and these latter stacks are algebraic. Our main theorems
pertain to the height stratification relative to fixed prime p on the stacks of
formal Lie groups and of n-buds. Notably, we show that the stack of n-buds of
height >= h is smooth and universally closed over F_p of dimension -h; we
characterize the stratum of n-buds of (exact) height h and the stratum of
formal Lie groups of (exact) height h as classifying stacks of certain groups,
smooth algebraic in the bud case; and we obtain some structure results on these
groups. We also obtain a second characterization of the stratum of formal Lie
groups of height h as an inverse limit of classifying stacks of certain finite
’etale algebraic groups. We conclude with a largely expository account of some
foundational material on limits in bicategories. | Source: | arXiv, 0708.3326 | Services: | Forum | Review | PDF | Favorites |
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