Hot-keys on this page
r m x p toggle line displays
j k next/prev highlighted chunk
0 (zero) top of page
1 (one) first highlighted chunk
r""" Modular abelian varieties """ from __future__ import absolute_import #***************************************************************************** # Copyright (C) 2005 David Kohel <kohel@maths.usyd.edu> # William Stein <wstein@math.ucsd.edu> # 2008-2009 Nicolas M. Thiery <nthiery at users.sf.net> # # Distributed under the terms of the GNU General Public License (GPL) # http://www.gnu.org/licenses/ #******************************************************************************
from .category_types import Category_over_base from .category_with_axiom import CategoryWithAxiom from .homsets import HomsetsCategory from .rings import Rings from .sets_cat import Sets
class ModularAbelianVarieties(Category_over_base): """ The category of modular abelian varieties over a given field.
EXAMPLES::
sage: ModularAbelianVarieties(QQ) Category of modular abelian varieties over Rational Field """ def __init__(self, Y): """ TESTS::
sage: C = ModularAbelianVarieties(QQ) sage: C Category of modular abelian varieties over Rational Field sage: TestSuite(C).run()
sage: ModularAbelianVarieties(ZZ) Traceback (most recent call last): ... assert Y.is_field() AssertionError """
def base_field(self): """ EXAMPLES::
sage: ModularAbelianVarieties(QQ).base_field() Rational Field """
def super_categories(self): """ EXAMPLES::
sage: ModularAbelianVarieties(QQ).super_categories() [Category of sets] """
class Homsets(HomsetsCategory):
class Endset(CategoryWithAxiom): def extra_super_categories(self): """ Implement the fact that an endset of modular abelian variety is a ring.
EXAMPLES::
sage: ModularAbelianVarieties(QQ).Endsets().extra_super_categories() [Category of rings] """ |