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  1. One reason to believe the Hodge conjecture is that it suggests a close relation between Hodge theory and algebraic cycles, and this hope has led to a long series of discoveries about algebraic cycles.[1]
  2. Hodge theory has become an important tool in algebraic geometry, particularly through its connection to the study of algebraic cycles.[2]
  3. While Hodge theory is intrinsically dependent upon the real and complex numbers, it can be applied to questions in number theory.[2]
  4. In arithmetic situations, the tools of p-adic Hodge theory have given alternative proofs of, or analogous results to, classical Hodge theory.[2]
  5. This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject.[3]
  6. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps.[3]
  7. This exposition of Hodge theory is a slightly retooled version of the authors Harvard minor thesis, advised by Professor Joe Harris.[4]
  8. Introduction Our objective in this exposition is to state and prove the main theorems of Hodge theory.[4]
  9. We then conclude the exposition by showing that Hodge theory can be used to give elegant proofs of the Date: March 8, 2018.[4]
  10. Next, we dene an operator that is, as its name will suggest, central to Hodge theory.[4]
  11. The recent work of Adiprasito–Huh–Katz establishes the Rota–Welsh Conjecture by developing a combinatorial Hodge theory for matroids in general.[5]
  12. Hodge–Tate representations are related to certain decompositions of p-adic cohomology theories analogous to the Hodge decomposition, hence the name p-adic Hodge theory.[6]
  13. This third symposium in the series focused on recent advances in all aspects of p-adic Hodge theory.[7]
  14. Another recurring theme at the symposium was the connection between p-adic Hodge theory and the local Langlands correspondence, modularity and number-theoretic applications.[7]
  15. The goal of the course is to give an introduction to the basic results in Hodge theory.[8]
  16. Hodge theory of compact, oriented, Riemannian manifolds 6.[8]
  17. Consider R C t (cid:55) g(tu + (1 t)w) MATH 731: HODGE THEORY 5 where w Cn is such that g(w) (cid:54)= 0.[8]
  18. We introduce real and complex Hodge theory to study topological invariants using harmonic analysis.[9]
  19. To do so, we review Riemannian and complex geometry, intro- duce de Rham cohomology, and give the basic theorems of real and complex Hodge theory.[9]
  20. Different faces of the Hodge theory Let M be a smooth compact manifold.[10]
  21. Hodge theory claims H k Each de Rham cohomology class contains a unique harmonic representative.[10]
  22. 1 2 LECTURE 26: THE HODGE THEORY The fact that these two statements are equivalent follows from Lemma 1.1.[10]
  23. 4 LECTURE 26: THE HODGE THEORY Now let , (M ) be two dierential forms on M .[10]
  24. The Banff International Research Station will host the "Equivariant Stable Homotopy Theory and p-adic Hodge Theory" workshop in Banff from March 1 to March 06, 2020.[11]
  25. The goal of p-adic Hodge theory is to classify and study p-adic representations of G p (i.e. l = p above) and to this end p-adic Hodge theory is astonishingly successful.[12]
  26. In this course, we will develop p-adic Hodge theory from the beginning and will provide complete proofs of many of the key results and theorems.[12]
  27. Working seminar on Hodge theory Spring 2020 Hodge theory is a beautiful and powerful subject, and the algebraic geometry prerequisites are minimal.[13]
  28. We recall that the almost purity theorem is one key technical ingredient in Faltings approach to p-adic Hodge theory, and we follow many of his ideas in this paper.[14]
  29. This is of course in analogy with classical Hodge theory, which is formulated most naturally in terms of complex-analytic spaces.[14]
  30. p-adic Hodge theory for rigid-analytic varieties 3 Let us rst explain our proof of this theorem.[14]
  31. We note that the idea of extracting many p-power roots is common to all known proofs of comparison theorems in p-adic Hodge theory.[14]

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  • [{'LOWER': 'hodge'}, {'LEMMA': 'theory'}]