Juvitop Seminar
Spring 2021
This semester Juvitop will be about The Galois Action on Symplectic KTheory.
We meet at 2:59 on Tuesday in zoom unless otherwise noted.

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The Galois Action on Symplectic KTheory by T. Feng, S. Galatius, and A. Venkatesh

The Galois Action on padic Symplectic KTheory talk by T. Feng
Introduction
Nat PachecoTallaj
Notes:
Discussion Section:
References:
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Dylan Wilson
Overview of (Ring) spectra, stable homotopy groups, infinite loop space machines, Postnikov truncations, Bott elements, Sduality, Moore spectra and homotopy with coefficients.
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Lucy Yang
Review and introduce the notions of algebraic Ktheory, symplectic Ktheory, and Hermitian Ktheory. Group completion and Ktheory spectra. Quillen's devissage and localization. Show how these three thoeries relate to eachother. Bottinverted Ktheory.
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Niven Achenjang
We start with a crash course on places/completions in algebraic number theory. We then give the statements of the main results of global class field, and look at some of their consequences. In particular, we show the existence of (narrow) Hilbert class fields.
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Daniel LiHuerta
Etale cohomology is an invariant for schemes that extends singular cohomology for varieties over C. After defining étale cohomology, we'll present several examples and computations to give a feel for the theory. We'll conclude by briefly introducing Thomason's spectral sequence, which relates étale cohomology to algebraic Ktheory, and mention how it's used in [FGV].
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Hodge Map and Witt Groups
Morgan Opie
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Grant Barkley
Notes:
We'll explain the basics of abelian varieties and the theory of complex multiplication. We use this to construct classes in symplectic Ktheory associated to a principally polarized abelian variety, and explain how complex multiplication can be used to parametrize a useful family of principally polarized abelian varieties for this purpose.
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Araminta Amabel
Notes:
We show that the map defined in last week’s talk is surjective. The result says that the socalled CM classes generate symplectic Ktheory groups in dimensions 4k2 for k>0. The proof involves techniques developed throughout the seminar, including a throw back to the Hodge and Betti maps.
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Yuri Sulyma
Appendix B.
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The Galois action on KSp and on CM abelian varieties
Zhiyu Zhang
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The main theorem and its proof: Part I
Peter Haine
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The main theorem and its proof: Part II
Vaughan McDonald
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Families of abelian varieties and stable homology
Sanath Devalapurkar
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This seminar is organized by Araminta Amabel, Nat PachecoTallaj, and Lucy Yang.