The integrality and zero-block conjecture for quadratic lattice extensions
Let L=M⊕NL=M\oplus NL=M⊕N be a quadratic lattice, where MMM is spanned by (e1,…,en−d)(e_1,\ldots,e_{n-d})(e1,…,en−d) and NNN by (en−d+1,…,en)(e_{n-d+1},\ldots,e_n)(en−d+1,…,en). Let L′=M′⊕NL'=M'\oplus NL′=M′⊕N be a lattice containing LLL in…