skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Lee, Heejong"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; ; ; ; ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract Let K / Q p K/\mathbf{Q}_{p}be unramified.Inside the Emerton–Gee stack X 2 \mathcal{X}_{2}, one can consider the locus of two-dimensional mod 𝑝 representations of Gal ⁢ ( K ̄ / K ) \mathrm{Gal}(\overline{K}/K)having a crystalline lift with specified Hodge–Tate weights.We study the case where the Hodge–Tate weights are irregular, which is an analogue for Galois representations of the partial weight one condition for Hilbert modular forms.We prove that if the gap between each pair of weights is bounded by 𝑝 (the irregular analogue of a Serre weight), then this locus is irreducible.We also establish various inclusion relations between these loci. 
    more » « less
    Full Text Available 
  2. ; ; (, Mathematika)
    Abstract Let and be natural numbers greater or equal to 2. Let be a homogeneous polynomial in variables of degree with integer coefficients , where denotes the inner product, and denotes the Veronese embedding with . Consider a variety in , defined by . In this paper, we examine a set of integer vectors , defined bywhere is a nonsingular form in variables of degree with for some constant depending at most on and . Suppose has a nontrivial integer solution. We confirm that the proportion of integer vectors in , whose associated equation  is everywhere locally soluble, converges to a constant as . Moreover, for each place of , if there exists a nonzero such that and the variety in admits a smooth ‐point, the constant is positive. 
    more » « less
    Full Text Available