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  1. Mar 11, 2005 · James Milne is a mathematician who has written books and articles on various topics. He also shares his photos of mountain areas, lakes and rivers, and New Zealand on his website.

    • Mathematics

      Mathematics site of J.S. Milne: course notes, preprints, and...

    • Michigan Lakes and Rivers

      Michigan site of J.S. Milne. Michigan lakes and rivers;...

    • NZ Mountains

      Photos of the New Zealand Lakes and Mountains - J.S. Milne...

    • Makalu

      Mountains site of J.S. Milne. Big Mountains Site --- J.S....

    • Books

      J. S. Milne's lecture notes on elliptic curves are already...

    • Course Notes

      All of Milne's books are really kind and very easy to read...

    • Abelian Varieties

      Abelian Varieties - J.S. Milne Top. Course Notes. Group...

    • Ant

      Current version (3.08) pdf file for printing (11pt; a4paper;...

    • What's New in Articles
    • What's New in Books
    • What's New in Course Notes
    • What's New in Expository Notes
    • What's New in Documents
    May 9, 2023. Classification of Mumford-Tate groups... v2
    Dec.23, 2022. Algebraic groups as automorphism...v3
    Dec.23, 2021. Tate and standard conjectures...
    Nov.12, 2020. Grothendieck's standard conjecture...
    Jan 2023. Elliptic Curves (2nd) available in paperback WSP
    October 2022. Fields and Galois Theoryavailable.
    April 2022. Algebraic Groups, corrected reprint + paperback.
    August 2020. Elliptic Curves, Second Edition. WSP
    Nov. 2, 2023. Corrected Algebraic Geometry AG
    June 23, 2021. Made source files available for GT and FT
    March 10, 2018. New version of Reductive Groups RG
    August 24, 2014. New version of Algebraic Geometry AG
    September 16, 2017. New version of Introduction to Shimura varieties
    September 5, 2016. Review of the Collected Works of John Tate
    July 2, 2015. The Riemann hypothesis over finite fields: from Weil to the present day.
    October 2021. Translations of three classic articles of Deligne.
    May 2021. Translation of letter of Langlands (2020-02-21)
    January 2021. Translation of Langlands's essay Funktorialität...
  2. James S. Milne (born 10 October 1942 in Invercargill, New Zealand) is a New Zealand mathematician working in arithmetic geometry.

  3. These are full notes for all the advanced (graduate-level) courses I have taught since 1986. Some of the notes give complete proofs (Group Theory, Fields and Galois Theory, Algebraic Number Theory, Class Field Theory, Algebraic Geometry), while others are more in the nature of introductory overviews to a topic.

  4. Office Information: Office Number: 3868. phone: 647-4471. Algebra and Algebraic Geometry; Number Theory; Mathematics.

  5. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology — those of base change, purity, Poincaré duality, and the Lefschetz trace formula.

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  7. Books. Étale Cohomology (PMS-33), Volume 33 James S. Milne. One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry.