On graded $${\mathbb {E}}_{\infty }$$-rings and projective schemes in spectral algebraic geometry

Derived Algebraic Geometry VII: Spectral Schemes

Derived Algebraic Geometry VII: Spectral Schemes

On Projective Geometry over Full Matrix Rings

1. K. L. Chung, Fluctuation of sums of independent random variables, Ann. of Math. vol. 51 (1950) pp. 697-706. 2. K. L. Chung and P. Erdos, Probability limit theorems assuming only the first moment. I, Memoirs of the American Mathematical Society, no. 6, pp. 13-19. 3.-, On the lower limit of sums of independent random variables, Ann. of Math. vol. 48 (1947) pp. 1003-1013. 4. K. L. Chung and W. ...

The rings of noncommutative projective geometry

In the past 15 years a study of “noncommutative projective geometry” has flourished. By using and generalizing techniques of commutative projective geometry, one can study certain noncommutative graded rings and obtain results for which no purely algebraic proof is known. For instance, noncommutative graded domains of quadratic growth, or “noncommutative curves,” have now been classified by geo...

Arc schemes in logarithmic algebraic geometry

ACKNOWLEDGEMENTS The development of this thesis has been strongly influenced by two mentors. Accordingly, I thank Kalle Karu, who introduced me to log arc schemes, posed the irreducibility question to me, and suggested the log motivic integration problem and offered uncounted hours of discussion about it; and I thank Karen Smith, who has carefully read and commented on the many various drafts o...