DSpace Community: KAIST Dept. of Mathematical SciencesKAIST Dept. of Mathematical Scienceshttp://hdl.handle.net/10203/5272017-05-28T23:04:31Z2017-05-28T23:04:31ZLocal universal lifting spaces of mod l Galois representationsChoi, Suh Hyunhttp://hdl.handle.net/10203/2234042017-05-08T08:43:31Z2017-07-01T00:00:00ZTitle: Local universal lifting spaces of mod l Galois representations
Authors: Choi, Suh Hyun
Abstract: Let p and l be distinct primes, K a finite extension of Q(p), and (rho) over bar : Gal((K) over bar /K)-> GL(n),((F) over barl) a mod l Galois representation. In this paper, we show that the generic fiber of universal lifting space of (rho) over bar is equidimensional of dimension n(2). We also characterize the irreducible components of the generic fiber of the universal lifting space which represent the liftings rho's of (rho) over bar with unipotent rho vertical bar I-K's, when pi', is trivial or n <= 4 and the square of the order of the residue field of K is not equal to 1 mod l. (C) 2017 Elsevier Inc. All rights reserved.2017-07-01T00:00:00ZCOLORFUL THEOREMS FOR STRONG CONVEXITYHolmsen, Andreas F.Karasev, Romanhttp://hdl.handle.net/10203/2236432017-05-15T05:16:51Z2017-06-01T00:00:00ZTitle: COLORFUL THEOREMS FOR STRONG CONVEXITY
Authors: Holmsen, Andreas F.; Karasev, Roman
Abstract: We prove two colorful Caratheodory theorems for strongly convex hulls, generalizing the colorful Caratheodory theorem for ordinary convexity by Imre Barany, the non-colorful Caratheodory theorem for strongly convex hulls by the second author, and the "very colorful theorems" by the first author and others. We also investigate if the assumption of a "generating convex set" is really needed in such results and try to give a topological criterion for one convex body to be a Minkowski summand of another.2017-06-01T00:00:00ZOn normalized generating sets for GQC codes over Z(2)Bae, SunghanKang, Pyung-LyunLi, Chengjuhttp://hdl.handle.net/10203/2236512017-05-15T05:17:24Z2017-05-01T00:00:00ZTitle: On normalized generating sets for GQC codes over Z(2)
Authors: Bae, Sunghan; Kang, Pyung-Lyun; Li, Chengju
Abstract: Let r(i), be positive integers and R-i = Z(2)[x]/ < x(ri) - 1 > for 1 <= i <= l. Denote R = R-1 x R-2 x ... x R-l. Generalized quasi-cyclic (GQC) code C of length (r(1), r(2),..., r(l)) over Z(2) can be viewed as Z(2) [x]-submodule of R. In this paper, we investigate the algebraic structure of C by presenting its normalized generating set. We also present a method to determine the normalized generating set of the dual code of C, which is derived from the normalized generating set of C. (C) 2016 Elsevier Inc. All rights reserved.2017-05-01T00:00:00ZCongruences of two-variable p-adic L-functions of congruent modular forms of different weightsChoi, Suh HyunKim, Byoung Duhttp://hdl.handle.net/10203/2236532017-05-15T05:17:27Z2017-05-01T00:00:00ZTitle: Congruences of two-variable p-adic L-functions of congruent modular forms of different weights
Authors: Choi, Suh Hyun; Kim, Byoung Du
Abstract: Vatsal (Duke Math J 98(2):397-419, 1999) proved that there are congruences between the p-adic L-functions (constructed by Mazur and Swinnerton-Dyer in Invent Math 25:1-61, 1974) of congruent modular forms of the same weight under some conditions. On the other hand, Kim (J Number Theory 144: 188-218, 2014), the second author, constructed two-variable p-adic L-functions of modular forms attached to imaginary quadratic fields generalizing Hida's work (Invent Math 79:159-195, 1985), and the novelty of his construction was that it works whether p is an ordinary prime or not. In this paper, we prove congruences between the two-variable p-adic L-functions (of the second author) of congruent modular forms of different but congruent weights under some conditions when p is a nonordinary prime for the modular forms. This result generalizes the work of Emerton et al. (Invent Math 163(3): 523-580, 2006), who proved similar congruences between the p-adic L-functions of congruent modular forms of congruent weights when p is an ordinary prime.2017-05-01T00:00:00Z