Equivariant -theory of Grassmannians II: the Knutson–Vakil conjecture

Equivariant Cohomology in Algebraic Geometry Lecture Eight: Equivariant Cohomology of Grassmannians Ii

σλ = |c T λi+j−i(Q− Fl+i−λi)|1≤i,j≤k. These determinants are variations of Schur polynomials, which we will call double Schur polynomials and denote sλ(x|y), where the two sets of variables are x = (x1, . . . , xk) and y = (y1, . . . , yn). (Here k ≤ n, and the length of λ is at most k.) Setting the y variables to 0, one recovers the ordinary Schur polynomials: sλ(x|0) = sλ(x). In fact, sλ(x|y)...

On the “main Conjecture” of Equivariant Iwasawa Theory

The “main conjecture” of equivariant Iwasawa theory concerns the situation where • l is a fixed odd prime number and K/k is a Galois extension of totally real number fields with k/Q and K/k∞ finite, where k∞/k is the cyclotomic Zl-extension (we set G = G(K/k) and Γk = G(k∞/k)), • S is a fixed finite set (which will normally be suppressed in the notation) of primes of k containing all primes whi...

Bigraded Cohomology of Z/2-equivariant Grassmannians

On the “main Conjecture” of Equivariant Iwasawa Theory

The “main conjecture” of equivariant Iwasawa theory concerns the situation where • l is a fixed odd prime number and K/k is a Galois extension of totally real number fields with k/Q and K/k∞ finite, where k∞/k is the cyclotomic Zl-extension (we set G = G(K/k) and Γk = G(k∞/k)), • S is a fixed finite set (which will normally be suppressed in the notation) of primes of k containing all primes whi...

On the Equivariant Main Conjecture of Iwasawa Theory

Refining results of David Burns and Cornelius Greither, respectively Annette Huber and Guido Kings, we formulate and prove an equivariant version of the main conjecture of Iwasawa theory for abelian number fields.