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001 ocn648765052;

003 OCoLC;

005 20141212052055.0;

006 m d ;

007 cr bn|||||||||;

008 100719s2010 ncu ob 000 0 eng d;

035 a| (Sirsi) o648765052;

035 a| (OCoLC)648765052;

040 a| EREc| EREd| EREd| UtOrBLW;

049 a| EREE;

090 a| QA564;

100 1 a| Hampton, Earl F.?| UNAUTHORIZED;

245 12 a| A primer for the foundations of algebraic geometry /c| by Earl F. Hampton.;

260 a| [Greenville, N.C.] :b| East Carolina University,c| 2010.;

300 a| 84 pages :b| digital, PDF file;

336 a| text2| rdacontent;

337 a| computer2| rdamedia;

338 a| online resource2| rdacarrier;

500 a| Presented to the faculty of the Department of Mathematics.;

500 a| Advisor: M Ravi.;

500 a| Title from PDF t.p. (viewed Sep. 9, 2010).;

502 b| M.A.c| East Carolina Universityd| 2010.;

504 a| Includes bibliographical references.;

520 3 a| The purpose of this thesis is to define the basic objects of study in algebraic geometry, namely, schemes and quasicoherent sheaves over schemes. We start by discussing algebraic sets as common zeros of polynomials and prove Hilbert's Nullstellensatz to establish a correspondence between algebraic sets and ideals in a polynomial ring. We then discuss just enough category theory to define a sheaf as a contravariant functor and then introduce ringed spaces, the spectrum of a ring, and the definition of affine schemes. We then discuss sheaves of modules over schemes. We then define projective varieties as ringed spaces. We end by proving Hilbert's syzygy theorem that can be used to study the equations defining projective varieties.;

538 a| System requirements: Adobe Reader.;

538 a| Mode of access: World Wide Web.;

650 0 a| Geometry, Algebraic.=| ^A42380;

650 0 a| Schemes (Algebraic geometry)=| ^A139230;

650 0 a| Categories (Mathematics)=| ^A23638;

650 0 a| Sheaf theory.=| ^A30429;

653 a| Mathematics;

700 1 a| Ravi, M. S.?| UNAUTHORIZED;

710 2 a| East Carolina University.b| Department of Mathematics.?| UNAUTHORIZED;

856 40 z| Access via ScholarShipu| http://hdl.handle.net/10342/2797;

949 o| jgml;

994 a| C0b| ERE;

596 a| 1 4;

998 a| 2284741;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 2284741-1001l| JNETm| JOYNERr| Ys| Yt| JNE3ETDu| 7/19/2010x| ETDz| JERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 2284741-2001l| HSLELECm| HSLr| Ys| Yt| HEETDu| 7/19/2010x| ETDz| HERESOURCE;

A primer for the foundations of algebraic geometry / by Earl F. Hampton.

Author/creator	Hampton, Earl F.
Other author	Ravi, M. S.
Other author	East Carolina University. Department of Mathematics.
Format	Theses and dissertations
Publication Info	[Greenville, N.C.] : East Carolina University, 2010.
Description	84 pages : digital, PDF file
Supplemental Content	Access via ScholarShip
Subjects	Geometry, Algebraic. Schemes (Algebraic geometry) Categories (Mathematics) Sheaf theory.

Summary	The purpose of this thesis is to define the basic objects of study in algebraic geometry, namely, schemes and quasicoherent sheaves over schemes. We start by discussing algebraic sets as common zeros of polynomials and prove Hilbert's Nullstellensatz to establish a correspondence between algebraic sets and ideals in a polynomial ring. We then discuss just enough category theory to define a sheaf as a contravariant functor and then introduce ringed spaces, the spectrum of a ring, and the definition of affine schemes. We then discuss sheaves of modules over schemes. We then define projective varieties as ringed spaces. We end by proving Hilbert's syzygy theorem that can be used to study the equations defining projective varieties.
General note	Presented to the faculty of the Department of Mathematics.
General note	Advisor: M Ravi.
General note	Title from PDF t.p. (viewed Sep. 9, 2010).
Dissertation note	M.A. East Carolina University 2010.
Bibliography note	Includes bibliographical references.
Technical details	System requirements: Adobe Reader.
Technical details	Mode of access: World Wide Web.

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A primer for the foundations of algebraic geometry / by Earl F. Hampton.

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