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Algebraic number field
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591	ON HOMOTOPY TYPES OF LIMITS OF SEMI-ALGEBRAIC SETS AND ADDITIVE COMPLEXITY OF POLYNOMIALS SAL BARONE AND SAUGATA BASU Abstract. We prove that the number of homotopy types of limits of oneparameter semi-algebraic families Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2011-02-02 17:01:53 Mathematical structures Field theory Algebraic structures Algebraic geometry Homotopy group Homotopy theory Topology Homotopy Polynomial Abstract algebra Mathematics Algebra
592	Smooth Orders and Cryptographic Applications Carl Pomerance1 and Igor E. Shparlinski2 1 Department of Fundamental Mathematics, Bell Laboratories Murray Hill, NJ[removed], USA Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2005-03-02 15:21:08 Mathematical analysis Prime-counting function Prime number theorem Prime number Elliptic curve Riemann hypothesis Smooth number Elliott–Halberstam conjecture Algebraic number field Mathematics Analytic number theory Number theory
593	GROSS-ZAGIER REVISITED BRIAN CONRAD Contents 1. Introduction 2. Some properties of abelian schemes and modular curves Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2004-08-10 16:48:34 Elliptic curves Algebraic topology Field theory Abelian variety Group scheme Formal group Rational point Supersingular elliptic curve Frobenius endomorphism Abstract algebra Algebraic number theory Algebraic groups
594	BOUNDING THE EQUIVARIANT BETTI NUMBERS AND COMPUTING ´ CHARACTERISTIC OF THE GENERALIZED EULER-POINCARE SYMMETRIC SEMI-ALGEBRAIC SETS SAUGATA BASU AND CORDIAN RIENER Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2014-01-17 21:15:39 Algebraic topology Algebraic geometry Field theory Polynomials Betti number Homogeneous polynomial Algebraic variety Symmetric polynomial Real algebraic geometry Abstract algebra Algebra Mathematics
595	RAMIFIED DEFORMATION PROBLEMS BRIAN CONRAD Introduction The proof of the semistable Taniyama-Shimura Conjecture by Wiles [22] and Taylor-Wiles [21] uses as its central tool the deformation theory of Galois representation Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2004-08-12 00:22:25 Algebraic number theory Galois theory Frobenius endomorphism Galois module Group scheme Dieudonné module Étale morphism Finite field Abstract algebra Algebra Algebraic groups
596	Discrete Comput Geom 30:65–[removed]DOI: [removed]s00454[removed]Discrete & Computational Geometry Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:35:46 Field theory Algebraic topology Betti number Topological graph theory Algebraic number theory Algebraic geometry Field extension Field Intersection number Abstract algebra Mathematics Algebra
597	POLYNOMIAL HIERARCHY, BETTI NUMBERS AND A REAL ANALOGUE OF TODA’S THEOREM SAUGATA BASU AND THIERRY ZELL Abstract. Toda [36] proved in 1989 that the (discrete) polynomial time hierarchy, PH, is contained in the class P# Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:44:12 Field theory Real algebraic geometry Algebraic geometry Real closed field Betti number Polynomial Algebraic variety Field Semialgebraic set Abstract algebra Mathematics Algebra
598	AN ASYMPTOTICALLY TIGHT BOUND ON THE NUMBER OF SEMI-ALGEBRAICALLY CONNECTED COMPONENTS OF REALIZABLE SIGN CONDITIONS SAUGATA BASU, RICHARD POLLACK, AND MARIE-FRANC ¸ OISE ROY Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:35:24 Algebraic topology Field theory Betti number Topological graph theory Algebraically closed field Holomorphic functional calculus Mathematics Abstract algebra Algebra
599	REFINED BOUNDS ON THE NUMBER OF CONNECTED COMPONENTS OF SIGN CONDITIONS ON A VARIETY SAL BARONE AND SAUGATA BASU Abstract. Let R be a real closed field, P, Q ⊂ R[X1 , . . . , Xk ] finite subsets of polynomials, with th Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2011-11-06 10:09:22 Algebraic geometry Commutative algebra Field extension Algebraic variety Algebraically closed field Zariski topology Betti number Puiseux series Algebraic closure Abstract algebra Algebra Field theory
600	RECIPROCITY LAWS. FROM EULER TO EISENSTEIN REVIEWER P. SHIU Fermat found that primes p ≡ 1 (mod 4) are sums of two squares, and Euler went on to investigate the representation of primes using more general quadratic for Add to Reading List Source URL: www.rzuser.uni-heidelberg.de Language: English - Date: 2002-11-03 20:34:30 Algebraic number theory Modular arithmetic Quadratic residue Mental calculators Disquisitiones Arithmeticae Quadratic reciprocity Reciprocity law Legendre symbol Class field theory Mathematics Abstract algebra Number theory

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