Cohomology of congruence subgroups of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="normal">SL</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>, Steinberg modules, and real quadratic fields

dedekind modules and dimension of modules

در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...

Cryptography in Real Quadratic Congruence Function Fields

The Diffie-Hellman key exchange protocol as well as the ElGamal signature scheme are based on exponentiation modulo p for some prime p. Thus the security of these schemes is strongly tied to the difficulty of computing discrete logarithms in the finite field Fp. The Diffie-Hellman protocol has been generalized to other finite groups arising in number theory, and even to the sets of reduced prin...

CONGRUENCE SUBGROUPS AND TWISTED COHOMOLOGY OF SLn(F [t℄) II: FINITE FIELDS AND NUMBER FIELDS

Equivalences between Elliptic Curves and Real Quadratic Congruence Function Fields

In 1994, the well-known Diie-Hellman key exchange protocol was for the rst time implemented in a non-group based setting. Here, the underlying key space was the set of reduced principal ideals of a real quadratic number eld. This set does not possess a group structure, but instead exhibits a so-called infrastructure. More recently, the scheme was extended to real quadratic congruence function e...

CONGRUENCE SUBGROUPS AND TWISTED COHOMOLOGY OF SLn(F [t])

for all n ≥ 2. Here, we study the extent to which this isomorphism holds when the trivial Z coefficients are replaced by some rational representation of SLn(F ). The group SLn(F [t]) acts on such a representation via the map SLn(F [t]) t=0 −→ SLn(F ). There are two approaches one might take. The first is to use the spectral sequence associated to the action of SLn(F [t]) on a certain Bruhat–Tit...