Richard Swan

Q: What Schools Are Affiliated With Richard Swan

Richard Swan is affiliated with the following schools: Princeton University, University of Chicago, Stanford University

Richard Swan's AcademicInfluence.com Rankings

Richard Swan

Mathematics

#1498

World Rank

#2447

Historical Rank

#616

USA Rank

Measure Theory

#1094

World Rank

#1407

Historical Rank

#400

USA Rank

mathematics Degrees

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Mathematics

Richard Swan's Degrees

PhD Mathematics Princeton University
Masters Mathematics Stanford University

Why Is Richard Swan Influential?

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According to Wikipedia, Richard Gordon Swan is an American mathematician who is known for the Serre–Swan theorem relating the geometric notion of vector bundles to the algebraic concept of projective modules, and for the Swan representation, an l-adic projective representation of a Galois group. His work has mainly been in the area of algebraic K-theory.

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Richard Swan's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Vector bundles and projective modules (1962) (567)
Induced Representations and Projective Modules (1960) (318)
Periodic Resolutions for Finite Groups (1960) (274)
Factorization of polynomials over finite fields. (1962) (232)
Generators and relations for certain special linear groups (1968) (226)
K-Theory of Finite Groups and Orders (1970) (206)
The Whitehead group of a polynomial extension (1964) (204)
Invariant rational functions and a problem of Steenrod (1969) (177)
Groups of cohomological dimension one (1969) (166)
Algebraic K-Theory (1968) (150)
Projective modules over Laurent polynomial rings (1978) (127)
Noether’s Problem in Galois Theory (1983) (125)
The Grothendieck ring of a finite group (1963) (117)
Hochschild cohomology of quasiprojective schemes (1996) (114)
Topological examples of projective modules (1977) (98)
K-Theory of quadric hypersurfaces (1985) (98)
Minimal resolutions for finite groups (1965) (90)
A new method in fixed point theory (1959) (88)
Vector bundles over affine surfaces (1976) (86)
A cancellation theorem for projective modules in the metastable range (1974) (85)
The $p$-period of finite group (1960) (83)
Projective Modules Over Group Rings and Maximal Orders (1962) (81)
The theory of sheaves (1964) (75)
The number of generators of a module (1967) (59)
Excision in algebraic K-theory (1971) (58)
A class of projective modules which are nearly free (1975) (47)
Some relations between higher K-functors (1972) (45)
On the Homotopy Type of Certain Two‐Dimensional Complexes (1961) (43)
Projective modules over binary polyhedral groups. (1983) (43)
AN APPLICATION OF GRAPH THEORY TO ALGEBRA (1963) (42)
Unique comaximal factorization (2004) (41)
On Stably Free Modules over Affine Algebras (2011) (38)
Representations of polycyclic groups (1967) (34)
Zero cycles on quadric hypersurfaces (1989) (33)
THE NONTRIVIALITY OF THE RESTRICTION MAP IN THE COHOMOLOGY OF GROUPS (1960) (32)
n-generator ideals in Prüfer domains (1984) (24)
Thom's theory of differential forms on simplical sets (1975) (24)
Hilbert''''s theorem on positive ternary quartics (1999) (21)
XVIII. Vector Bundles, Projective Modules and The K-Theory of Spheres (1988) (21)
Groups with periodic cohomology (1959) (20)
A Simple Proof of Rankin's Campanological Theorem (1999) (18)
Cup products in sheaf cohomology, pure injectives, and a substitute for projective resolutions (1999) (15)
Groups with no odd dimensional cohomology (1971) (15)
The homology of cyclic products (1959) (14)
Projective modules over finite groups (1959) (14)
Determinantal Ideals, Pfaffian Ideals, and the Principal Minor Theorem (2007) (14)
K 2 (R) (1968) (13)
Torsion free cancellation over orders (1988) (13)
The Stable Rank of Topological Algebras and a Problem of R.g. Swan (1998) (13)
THE FLABBY CLASS GROUP OF A FINITE CYCLIC GROUP (2007) (13)
Algebraic Vector Bundles on the 2-Sphere (1993) (13)
NONABELIAN HOMOLOGICAL ALGEBRA AND K-THEORY (1970) (11)
Correction to “An application of graph theory to algebra” (1969) (11)
On maps with nonnegative Jacobian. (1959) (10)
Linear maps over abelian group algebras (1995) (9)
K-theory of coherent rings (2019) (9)
Two counterexamples in Power Series Rings (1986) (8)
Shorter Notes: Representations of Polycyclic Groups (1967) (7)
A Splitting Principle in Algebraic K - theory (1971) (6)
Failure of cancellation for direct sums of line bundles (1993) (5)
Quaternionic Bundles on Algebraic Spheres (1996) (5)
K-theory and algebraic correspondences (1973) (5)
TARSKI ’ S PRINCIPLE AND THE ELIMINATION OF QUANTIFIERS (2005) (5)
A simple proof of Gabber’s theorem on projective modules over a localized local ring (1988) (4)
A Special Type of Invertible Ideal (2005) (4)
A SIMPLE PROOF OF THE CUP PRODUCT REDUCTION THEOREM. (1960) (4)
Another proof of the quadratic reciprocity theorem (1990) (4)
Non-self-dual Stably Free Modules (2010) (3)
Relations between algebraic and topological K theory (1968) (3)
EXCERPT FROM ON SOME ACTIONS OF STABLY ELEMENTARY MATRICES ON ALTERNATING MATRICES (2007) (2)
Factorizations of Monic Polynomials (2004) (2)
Conference on Commutative Algebra, 1975 : [papers] (1975) (2)
Symplectic Modules and von Neumann Regular Matrices over Commutative Rings (2010) (2)
On the straightening law for minors of a matrix (2016) (2)
SOME STABLY FREE MODULES WHICH ARE NOT SELF DUAL (2006) (2)
Krull-Schmidt theorems and applications (1968) (1)
K-theory and stable algebra (p. 5 à 60) . The Whitehead group of a polynomial extension (p. 61 à 80) (1964) (1)
Definition of G(R) and examples (1968) (1)
Sums of Alternating Matrices and Invertible Matrices (2008) (1)
Serre's theorem (1968) (1)
GOLDIE’S THEOREM (2005) (1)
Spec (R) and H(R) (1968) (1)
Definition of KO(A) and some examples (1968) (1)
The connection between KO(R) and GO(R) (1968) (1)
The exact sequence of Ki's (1968) (1)
Localization and relation between GO(R) and GO(RS) (1968) (1)
Further results on K1 and K0 (1968) (1)
EXCERPT FROM A REGENERATIVE PROPERTY OF A FIBRE OF INVERTIBLE ALTERNATING MATRICES (2007) (1)
K1 and G1 (1970) (0)
Higher G-Theory of Nilpotent Grobt S (1988) (0)
On Stably Free Modules over Affine Algebras (2012) (0)
A Simple Proof of Rankin's (2016) (0)
Basic topological remarks (1968) (0)
K F-theory of Categories (2010) (0)
Book Review: The cohomology of groups (1993) (0)
KO of graded rings (1968) (0)
Simply-laced isomonodromy systems . On the functions counting walks with small steps in the quarter plane . The structure of approximate groups . On stably free modules over affine algebras . Perfectoid spaces (2012) (0)
Book Review: Serre's problem on projective modules (2008) (0)
K0 of a maximal order (1970) (0)
Picard group and the determinant (1968) (0)
ON A THEOREM OF MOHAN KUMAR AND NORI (2007) (0)
Results on K0 and G0 (1970) (0)
Chain complexes and the nilpotence of of (1968) (0)

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What Schools Are Affiliated With Richard Swan?

Richard Swan is affiliated with the following schools:

Richard Swan's Academic­Influence.com Rankings