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2 results

  • 1 - Unoriented Bordism

  • Eric Peterson, Harvard University, Massachusetts
  • Book:
    Formal Geometry and Bordism Operations
    Published online:
    23 November 2018
    Print publication:
    06 December 2018, pp 9-48

  • Summary

    We recast Thom’s classical calculation of the unoriented bordism ring in the language of formal geometry, introducing foundational concepts as we go along, especially: Thom spectra and the Thom isomorphism, formal schemes, and the formal-geometric perspectives on the Steenrod algebra and on the Adams spectral sequence. This chapter is designed primarily with pedagogy in mind, as this calculation introduces all of the main structures used in the rest of the book, restricted to a particularly simple context.

  • Un résultat de connexité pour les variétés analytiques p-adiques: privilège et noethérianité

  • Part of
  • Jérôme Poineau
  • Journal:
    Compositio Mathematica / Volume 144 / Issue 1 / January 2008
    Published online by Cambridge University Press:
    01 January 2008, pp. 107-133
    Print publication:
    January 2008
    • Article
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  • Let k be a non-Archimedean field, let X be a k-affinoid space and let f1,…,fn, with , be analytic functions over X. If X is irreducible, we prove that the analytic domain is still irreducible, provided that is small enough. Then, for a general X, we precisely describe how the geometric connected components of the spaces behave with regards to ε. Finally, we obtain a result concerning privileged neighbourhoods and adapt a theorem from complex analytic geometry about Noetherianity for germs of analytic functions.