# Christopher Lazda

## Preprints

1. A Néron-Ogg-Shafarevich criterion for K3 surfaces (joint with B. Chiarellotto and C. Liedtke) arXiv pdf
2. A note on effective descent for overconvergent isocrystals arXiv pdf
3. A homotopy exact sequence for overconvergent isocrystals (joint with A. Pál) arXiv pdf
4. Cycle classes in overconvergent rigid cohomology and a semistable Lefschetz $$(1,1)$$ theorem (joint with A. Pál) arXiv pdf

## Accepted

1. Fundamental groups and good reduction criteria for curves over positive characteristic local fields, to appear in J. Théor. Nombres Bordeaux arXiv pdf

## Journal Articles

1. Around $$\ell$$-independence (joint with B. Chiarellotto), Compos. Math. (2016) 154 (1): 223-248 article arXiv pdf
2. Combinatorial degenerations of surfaces and Calabi-Yau threefolds (joint with B. Chiarellotto), Algebra & Number Theory (2016) 10 (10): 2235-2266 article arXiv pdf
3. Incarnations of Berthelot's conjecture, J. Number Theory (2016) 166: 137-157 article arXiv pdf
4. Relative fundamental groups and rational points, Rend. Sem. Mat. Univ. Padova (2015) 134: 1-45 article arXiv pdf
5. Rigid rational homotopy types, Proc. London Math. Soc. (2014) 109 (2): 523-551 article arXiv pdf

## Monographs

1. Rigid Cohomology over Laurent Series Fields (joint with A. Pál), Springer (2016) vol. 21 of Algebra and Applications book

## Theses

1. Rational homotopy theory in arithmetic geometry, applications to rational points thesis pdf
My Ph.D. thesis, the first two chapters of which are entirely contained in "Relative fundamental groups and rational points" and "Rigid rational homotopy types" above.
2. 2-Descent on the Jacobins of Hyperelliptic Curves pdf
My essay for Part III of the Mathematical Tripos at Cambridge.

## Other Documents

1. Rigid cohomology over Laurent series fields (joint with A. Pál)
• I: First definitions and basic properties arXiv pdf
• II: Finiteness and Poincaré duality for smooth curves arXiv pdf
• III: Absolute coefficients and arithmetic applications arXiv pdf
• These are earlier versions of chapters from our book on rigid cohomology. The book itself contains far more material, and much stronger results.