1,357,279 research outputs found
Card from Emiko Satake to Mitzi Naohara
No full textA Christmas card from Emiko Satake who was Mitzi Masukawa Naohara's student in the nursery and kindergarten in the Poston camp in Arizona. It was probably sent to Mitzi while she was incarcerated at the Poston camp. The caption reads: Pupil in Nursery 2 yrs, kdgtn. 1yr, relocated Utah. An item from: Mitzi Naohara scrapbook (csudh_nao_0400), page 23.The George and Mitzi Naohara Papers consists of photo albums and scrapbooks compiled by George and Mitzi Naohara, and other documents pertaining to the Naohara and Masukawa family. Contained are photographs, correspondence, documents, and memorabilia depicting their experiences during World War II. George Nobuo Naohara is a Kibei Nisei, and his experiences include his farm labor in Idaho and Utah, incarceration in the Manzanar, Jerome, and Tule Lake camps, and the U.S. Army language school training and Korean War. He also engaged in Buddhist activities for his whole life and there are moving images depicting Gardena Buddhist Church activities after the war. Mitzi Masukawa Naohara was a preschool teacher at the Poston camp, Arizona, and also a member of a young Nisei women's club, "Sigma Debs.” Her collected materials depict her life as a teacher and social events in the Poston camp during the war
The Kuga-Satake Construction: A Modular Interpretation
No full textGiven a polarized complex K3 surface, one can attach to it a complex abelian variety,
called Kuga-Satake variety. The Kuga-Satake variety is determined by the singular
cohomology of the K3 surface; on the other hand, this singular cohomology can be
recovered by means of the weight 1 Hodge structure associated to the Kuga-Satake
variety. Despite the transcendental origin of this construction, Kuga-Satake varieties
have interesting arithmetic properties. Kuga-Satake varieties of K3 surfaces defined
over number fields descend to finite extension of the field of definition. This property
suggests that the Kuga-Satake construction can be interpreted as a map between
moduli spaces. More precisely, one can define a morphism, called Kuga-Satake map,
between the moduli space of K3 surfaces and the moduli space of abelian varieties
with polarization and level structure. This morphism, defined over a number field,
is obtained by regarding the classical construction as a map between an orthogonal
Shimura variety, closely related to the moduli space of K3 surfaces, and the Siegel
modular variety. The most remarkable fact is that the Kuga-Satake map extends
to positive characteristic for almost all primes, associating to K3 surfaces abelian
varieties over finite fields. This can be proven applying a result by Faltings on the
extension of abelian schemes and the good reduction property of Kuga-Satake varieties
A modular ramified geometric Satake equivalence
No full textWe extend the ramified geometric Satake equivalence due to Zhu (for tamely ramified groups) and the third named author (in full generality) from rational coefficients to include modular and integral coefficients
Y. Satake
No full textSatake working on some documents at a desk.Inscriptions on image and/or album page: "Y. Satake/Physiological Lab., Sender"Digitized by: MBLWHOI Libraryimage/jpg black and white image reformatted digitalPhotograph
ON THE SATAKE ISOMORPHISM
No full textAbstract
In a 1983 paper, the author has established a (decategorified) Satake equivalence for affine Hecke algebras. In this paper, we give new proofs for some results of that paper, one based on the theory of J-rings and one based on the known character formula for rational representations of a reductive group in positive, large characteristic. We also give an extension of that formula to disconnected groups
Lorentzian and Octonionic Satake equivalence
No full textWe establish a derived geometric Satake equivalence for the real group (resp. ), to be called the Lorentzian Satake equivalence (resp. Octonionic Satake equivalence). By applying the real-symmetric correspondence for affine Grassmannians, we obtain a derived geometric Satake equivalence for the splitting rank symmetric variety (resp. ). As an application, we compute the stalks of the -complexes for spherical orbit closures in the real affine Grassmannian for and the loop space of . We show the stalks are given by the Kostka-Foulkes polynomials for (resp. ) but with replaced by (resp. )
Cubic Fourfolds and the Kuga-Satake Construction
No full textGiven a K3 surface S, the Kuga-Satake construction associates to S an abelian variety KS(S) known as the Kuga-Satake variety. Many similarities between cubic fourfolds X and K3 surfaces S have been studied, particularly via Hodge theory by Hassett and derived categories by Kuznetsov. We study how the Kuga-Satake construction fits into this theory by studying the Kuga-Satake varieties of cubic fourfolds and their associated K3 surfaces, endormorphism algebras of cubic fourfolds, and the derived category D^b(KS(S)).Thesis (Ph.D.)--Michigan State University. Mathematics - Doctor of Philosophy, 2023Includes bibliographical reference
Extensions of the Euler-Satake Characteristic of Closed 3-Orbifolds
No full textThe author granted permission for the digitization of this paper. It was submitted by CD.The project described here is a continuation of the work of several authors on orbifold
invariants in low-dimensional and algebraic topology. Speci cally, my research
explores applying the Euler-Satake characteristic to the {sectors of an orbifold for
a nitely-generated group which results in a numerical invariant of the original
orbifold, the {Euler-Satake characteristic. Most Euler characteristics have proven
ine ective in giving useful information on orbifolds and, in particular, 3{orbifolds.
Orbifolds can be partitioned into two categories: orientable and non-orientable. This
partition is determined by the types of singularities in the orbifolds. My work previous
to this project has dealt with formulating this invariant for orientable 3{orbifolds
which lead to the successful determination of their point singularities when = F`,
the free group of ` generators (see [3]). By now considering non-orientable 3{orbifolds,
we have developed a formulation of the {Euler{Satake characteristic for all closed,
e ective 3{orbifolds. In light of these formulas, counterexamples exist to show that
neither an in nite collection of F`{ nor Z`{Euler{Satake characteristics determine
the point singularities of general closed 3{orbifolds. Furthermore, counterexamples
exist which prove that even an in nite collection of both F`{ and Z`{Euler{Satake
characteristics do not determine the point singularities of general closed 3{orbifolds.This paper was read and approved by Drs. Christopher Seaton, Rachel Dunwell, David Rupke, and Michael Sheard
Integral points on symmetric varieties and Satake compatifications
No full textLet be an affine symmetric variety defined over . We compute the asymptotic distribution of the angular components of the integral points in . This distribution is described by a family of invariant measures concentrated on the Satake boundary of . In the course of the proof, we describe the structure of the Satake compactifications for general affine symmetric varieties and compute the asymptotic of the volumes of norm balls.Let be an affine symmetric variety defined over . We compute the asymptotic distribution of the angular components of the integral points in . This distribution is described by a family of invariant measures concentrated on the Satake boundary of . In the course of the proof, we describe the structure of the Satake compactifications for general affine symmetric varieties and compute the asymptotic of the volumes of norm balls
Two monoidal structures on Satake category in mixed characteristic
No full textFargues and Scholze proved the geometric Satake equivalence over the
Fargues-Fontaine curve. This can be transferred to the geometric Satake
equivalence concerning a Witt vector affine Grassmannian via nearby cycle. On
the other hand, Zhu proved the geometric Satake equivalence concerning a Witt
vector affine Grassmannian. In this paper, we explain the coincidence of these
two geometric Satake equivalences, including the coincidence of the two
symmetric monoidal structures on the Satake category.Comment: 20 page
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